System and methods for optimized drug delivery and progression of diseased and normal cells

ABSTRACT

System for recommending an optimal treatment protocol for a specific individual are disclosed. The systems comprise generally a system model, a plurality of treatment protocols, a system model modifier, wherein said system model is modified by the system model modifier based on parameters specific to the individual; and a selector to select an optimal treatment protocol from said plurality of treatment protocols based on the modified system model. Systems embodying the above techniques but for a general patient are also disclosed. Systems for a general patient and an individual for various specific diseases are disclosed. Methods and computer program products embodying the above techniques are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional of pending U.S. application Ser. No. 11/390,250filed Mar. 28, 2006, which is a Divisional application of U.S.application Ser. No. 10/192,001 filed Jul. 10, 2002, which issued asU.S. Pat. No. 7,266,483, which is a Divisional application of U.S.application Ser. No. 09/691,053 filed Oct. 19, 2000, which issued asU.S. Pat. No. 6,871,171. The entire disclosures of the priorapplications are hereby incorporated by reference.

I. DESCRIPTION OF THE INVENTION

I.A. Field of the Invention

The present invention relates generally to prediction of a progressionof healthy and diseased cells in patients with/without treatment effectincorporated therein. The present invention is embodied in systems,methods and computer program products for predicting the progression ofa biological system, and for prediction and optimization of treatment ofdisease. These systems, methods and computer program products can beused to simulate a general patient for the use in certain stages in drugdevelopment and trials as well as for an individual patient.

I.B. Background of the Invention

It is well known that when drugs are administered to combat diseases,they do not differentiate between healthy and diseased cells. The drugsare often toxic to healthy cells as well, Therefore, in prescribing aspecific treatment protocol, it is necessary to consider the effect ofthe treatment protocol on both healthy cells as well as diseased cells.

Mathematical models that model biological systems are well known in theart. A wide variety of models are known including those that useordinary differential equations, partial differential equations and thelike, More specifically, these mathematical models can simulate celllines, tumor growth, etc. Conventionally, these models have been usedfor prediction of treatment results. However, such conventionalpredictive models generally employ an analytical approach, in whichgeneralizations about the effect of the treatment protocols on a diseasemust be made. This approach, while providing useful general information,cannot be used to predict results of treatment in realisticcircumstances. Thus, techniques that include more complex and detailedscenarios are needed.

II. SUMMARY OF THE INVENTION

It is an objective of the present invention to provide techniques forrecommending optimal treatments for a general patient and a specificindividual patient.

It is another objective of the invention to provide techniques forpredicting the progress of biological processes in a general patient anda specific individual patient under a variety of treatment protocols aswell as under no treatment.

It is yet another objective of the present invention to providetechniques for modelling various specific biological processes for ageneral patient and a specific individual patient under a plurality oftreatment protocols including no treatment.

To meet the objectives of the present invention, there is provided asystem for recommending an optimal treatment protocol for an individualcomprising a system model, a plurality of treatment protocols, a systemmodel modifier. The system model is modified by the system modelmodifier based on parameters specific to the individual. The systemfurther comprises a selector to select an optimal treatment protocolfrom the plurality of treatment protocols based on the modified systemmodel.

Preferably the system model further comprises a realistic biologicalprocess model and a realistic treatment model that models the effects ofa treatment on the biological process.

Still preferably, the biological process model comprises mathematicalmodels for biological processes affecting healthy cell populations andbiological processes affecting cell populations with at least onedisease.

Still preferably the healthy cell populations include bone-marrow cellsand host tissue cells that are affected by the treatment model.

Still preferably the cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrompocyte cells.

Preferably, the treatment models comprise treatment specific processesthat affect cell population.

Still preferably the treatment specific process is interactionsinvolving one of a group comprising pharmacokinetic, pharmacodynamic,cytostatic, cytotoxic, and methods of affecting cell biology and causingcell death, with associated biological processes.

Preferably the parameters specific to the individual include one or moreselected from a group consisting of parameters related to the biologicalprocess' dynamics, patient specific drug PK, PD and dynamics ofdose-limiting host tissues.

Still preferably the parameters related to biological process' dynamicscomprise age, weight, gender, blood picture, desired length of treatmentprotocol, previous reaction to treatment, molecular markers, geneticmarkers, pathologic specifics and cytologic specifics.

Preferably the selector incorporates user-specific parameters inperforming selection.

Still preferably the incorporation is done by using a fitness function.

Still preferably the fitness function incorporates at least oneparameter selected from a group comprising patient survival, time todeath, time to reach a specified disease stage (including cure), tumorload, pathogen load, cytotoxicity, side effects, quality of life, costof treatment, and pain.

Still preferably a user can input specific coefficients for said atleast one parameter to adjust the fitness function to satisfy the user'sgoals.

Still preferably the user-specific parameters are based on a user, saiduser being a medical doctor.

Still preferably the user-specific parameters are based on a user, saiduser being a scientist.

Still preferably the user-specific parameters are based on a user, saiduser being a drug developer.

Preferably the selection of treatment protocols incorporate cytotoxiceffects.

Preferably the selection of treatment protocols incorporate drugefficacy.

Preferably the selector performs the selection using operation researchmethods.

Preferably the selector further comprises heuristics, said heuristicsbeing used to perform searching and selection.

Still preferably said heuristics comprise computational feasibility.

Preferably, the recommendation is a combination of disease and treatmentstrategy, including types of treatment, e.g. chemotherapy, radiotherapy,surgery, immunotherapy, etc, device, drug or drug combination andtreatment schedule and dosage.

Preferably the system is implemented over a distributed computingsystem.

Still preferably the distributed computing system is the Internet.

Still preferably a user uses the system remotely.

Another aspect of the present invention is a system for recommending anoptimal treatment protocol for a general patient comprising a systemmodel, a plurality of treatment protocols and a selector to select anoptimal treatment protocol from said plurality of treatment protocolsbased on the system model.

Preferably the system model further comprises a realistic biologicalprocess model and a realistic treatment model that models the effects ofa treatment on said biological process.

Still preferably, the biological process model comprises mathematicalmodels for biological processes affecting healthy cell populations andbiological processes affecting cell populations with at least onedisease.

Still preferably, the healthy cell populations include bone-marrow cellsand host tissue cells that are affected by said treatment model.

Still preferably, the cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrompocyte cells.

Still preferably, the treatment models comprise treatment specificprocesses that affect cell populations.

Still preferably, the treatment specific process is interactionsinvolving one of a group comprising pharmacokinetic, pharmacodynamic,cytostatic, cytotoxic, and methods of affecting cell biology and causingcell death, with associated biological processes.

Preferably the selector incorporates user-specific parameters inperforming selection.

Still preferably, the incorporation is done by using a fitness function.

Still preferably, the fitness function incorporates at least oneparameter selected from a group comprising patient survival, time todeath, time to reach a specified disease stage and cure, tumor load,pathogen load, cytotoxicity, side effects, quality of life, cost oftreatment and pain.

Still preferably, a user can input specific coefficients for said atleast one parameter to adjust the fitness function to satisfy the user'sgoals.

Still preferably, the user-specific parameters are based on a user, saiduser being a medical doctor.

Still preferably, the user-specific parameters are based on a user, saiduser being a scientist.

Still preferably, the user-specific parameters are based on a user, saiduser being a drug developer.

Preferably, the selection of treatment protocols incorporate cytotoxiceffects.

Preferably, the selection of treatment protocols incorporate drugefficacy.

Preferably, the selector performs the selection using operation researchmethods.

Preferably, the selector further comprises heuristics, said heuristicsbeing used to perform searching and selection.

Still preferably, the heuristics comprise computational feasibility.

Preferably, the recommendation is a combination of disease and treatmentstrategy, including types of treatment, e.g. chemotherapy, radiotherapy,surgery, immunotherapy, etc, device, drug or drug combination andtreatment schedule and dosage.

Preferably, the system is implemented over a distributed computingsystem.

Still preferably, the distributed computing system is the Internet.

Still preferably, a user uses the system remotely.

Still preferably, the remote system is a telephone.

Yet another aspect of the present invention is a system for predictingprogression of a biological process in an individual patient under aplurality of treatment protocols, wherein said biological process couldbe related to healthy or diseased processes, said plurality of protocolsincluding no treatment. The system comprises a system model, a pluralityof treatment protocols and a system model modifier. The system model ismodified by the system model modifier based on parameters specific tothe individual. The system further comprises a predictor to predict theprogression of at least one of the disease and the natural biologicalprocess under said plurality of treatment protocols based on themodified system model.

Preferably, the system model further comprises a realistic biologicalprocess model and a realistic treatment model that models the effects ofa treatment on said biological process.

Still preferably, the biological process model comprises mathematicalmodels for biological processes affecting healthy cell populations andbiological processes affecting cell populations with at least onedisease.

Still preferably, the healthy cell populations include bone-marrow cellsand host tissue cells that are affected by said treatment model.

Still preferably, the cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseased atleast one of Neutrophil cells and diseased Thrombocyte cells.

Still preferably, the treatment models comprise treatment specificprocesses that affect cell population.

Still preferably the treatment specific process is interactionsinvolving one of a group comprising PK, PD, cytostatic, cytotoxic, andmethods of affecting cell biology and causing cell death, withassociated biological processes.

Preferably the parameters specific to the individual include one or moreselected from a group consisting of parameters related to the biologicalprocess' dynamics, patient specific drug PK, PD and dynamics ofdose-limiting host tissues.

Still preferably, the parameters related to biological process' dynamicscomprise age, weight, gender, blood picture, desired length of treatmentprotocol, previous reaction to treatment, molecular markers, geneticmarkers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a system for predictingprogression of a biological process in a general patient under aplurality of treatment protocols, wherein said biological process couldbe healthy or diseased processes, said plurality of protocols includingno treatment. The system comprises a system model, a plurality oftreatment protocols and a predictor to predict the progression of thedisease or the natural biological process under said plurality oftreatment protocols.

Preferably, the system model further comprises a realistic biologicalprocess model and a realistic treatment model that models the effects ofa treatment on said biological process.

Still preferably, the biological process model comprises mathematicalmodels for biological processes affecting healthy cell populations andbiological processes affecting cell populations with at least onedisease.

Still preferably, the healthy cell populations include bone-marrow cellsas well as other host tissue cells that are affected by said treatmentmodel.

Still preferably, the cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrombocyte cells.

Still preferably, the treatment models comprise treatment specificprocesses that affect cell population.

Still preferably, the treatment specific process is interactionsinvolving one of a group comprising PK, PD, drug cytostatics, drugcytotoxics, and methods of affecting cell biology and causing celldeath, with associated biological processes.

Yet another aspect of the present invention is a system for modellingThrombopietic lineage in an individual, said system comprising aThrombopoiesis system model including a realistic process progressionmodel, for cells involved in Thrombopoiesis, said progression modelincluding multiplication and differentiation and a system modelmodifier, wherein said Thrombopoiesis system model is modified by thesystem model modifier based on parameters specific to the individual.

Preferably, the system model incorporates a realistic progression ofcells involved in diseased Thrombopoiesis.

Still preferably, the diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the system model incorporates effects of at least onedrug in the realistic progression of cells involved in Thrombopoiesis.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, the process model imitates a course of theindividual's bone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, said process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment can be chemotherapy.

Still preferably, the process model further comprises a plurality ofcompartments.

Still preferably, the compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis is included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the process model further incorporates the effects ofTPO on the SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomitosis.

Still preferably, when the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, in the CFU-Meg compartment the cells are sensitive toTPO concentration regardless of the concentration of TPO.

Still preferably the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, the SC compartment when the TPO concentration is abovethe threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, the platelet releasing cells contribute platelets tothe first sub-compartment of the PL compartment.

Preferably the model is used for recommending an optimal treatmentprotocol, wherein said system further comprises a plurality of treatmentprotocols and a selector to select an optimal treatment protocol fromsaid plurality of treatment protocols based on the modified systemmodel.

Yet another aspect of the present invention is a system for modellingThrombopietic lineage in a general patient, said system comprising aThrombopoiesis system model including a realistic process model forcells involved in Thrombopoiesis.

Preferably, the system model incorporates a realistic progression ofcells involved in diseased Thrombopoiesis.

Still preferably, the diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the system model incorporates effects of at least onedrug in the realistic progression of cells involved in Thrombopoiesis.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, the process model imitates a course of the patient'sbone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, the process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, the cell-suppressive treatment is chemotherapy.

Still preferably, the process model further comprises a plurality ofcompartments.

Still preferably, the compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis are included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the process model further incorporates the effects ofTPO on the SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomitosis.

Still preferably, when the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, the CFU-Meg compartment the cells are sensitive to TPOconcentration regardless of the concentration of TPO.

Still preferably, the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, in the SC compartment when the TPO concentration isabove the threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably, in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, the platelet releasing cells contribute platelets tothe first sub-compartment of the PL compartment.

Preferably, said model is used for recommending an optimal treatmentprotocol, wherein said system further comprises a plurality of treatmentprotocols; and a selector to select an optimal treatment protocol fromsaid plurality of treatment protocols based on the modified systemmodel.

Yet another aspect of the present invention is a system for predictingprogression of Thrombopoiesis and a model of Thrombocytopenia for anindividual under a plurality of treatment protocols, said plurality ofprotocols including no treatment, said system comprising aThrombopoiesis and a Thrombocytopenia system model, a plurality oftreatment protocols for affecting Thrombopoiesis and treatingThrombocytopenia using at least one drug, a system model modifier. TheThrombopoiesis and Thrombocytopenia system models are modified by thesystem model modifier based on parameters specific to the individual.The system further comprises a predictor to predict the progression ofthe disease or the natural biological process under said plurality oftreatment protocols based on the modified system model.

Preferably, the system model incorporates a realistic progression ofcells involved in diseased Thrombopoisis.

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the system model incorporates effects of at least onedrug on the realistic progression of cells involved in Thrombocytopenia.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, said process model imitates a course of theindividual's bone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, said process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Still preferably, said process model further comprises a plurality ofcompartments.

Still preferably, said compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis are included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the process model further incorporates the effects ofTPO on the SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomotisis.

Still preferably, the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, in the CFU-Meg compartment the cells are sensitive toTPO concentration regardless of the concentration of TPO.

Still preferably, the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, in the SC compartment when the TPO concentration isabove the threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably, in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, the platelet releasing cells contribute platelets tothe first sub-compartment of the PL compartment.

Yet another aspect of the present invention is a system for predictingprogression of Thrombopoiesis and a model of Thrombocytopenia for ageneral patient under a plurality of treatment protocols, said pluralityof protocols including no treatment. The system comprises aThrombopoiesis and a Thrombocytopenia system model, a plurality oftreatment protocols for affecting Thrombopoiesis and treatingThrombocytopenia using at least one drug; and a predictor to predict theprogression of the disease or the natural biological process under saidplurality of treatment protocols based on the modified system model.

Preferably the system model incorporates a realistic progression ofcells involved in diseased Thrombopoiesis

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the system model incorporates effects of at least onedrug in the realistic progression of cells involved in Thrombocytopenia.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, said process model imitates a course of theindividual's bone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, said process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Still preferably, said process model further comprises a plurality ofcompartments.

Still preferably, said compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis are included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the process model further incorporates the effects ofTPO on the SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomotisis.

Still preferably, when the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, in the CFU-Meg compartment the cells are sensitive toTPO concentration regardless of the concentration of TPO.

Still preferably, the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, in the SC compartment when the TPO concentration isabove the threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably, in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, wherein the platelet releasing cells contributeplatelets to the first sub-compartment of the PL compartment.

Another aspect of the present invention is a system for modellingNeutrophil lineage for an individual, said system comprising aNeutrophil system model including a realistic process model for cellsinvolved in Granulopoiesis and a system model modifier. The Neutrophilsystem model is modified by the system model modifier based onparameters specific to the individual.

Preferably, the system model incorporates a realistic progression ofcells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesis andNeutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF);

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters of the system.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Preferably, said model is used for recommending an optimal treatmentprotocol, wherein said system further comprises a plurality of treatmentprotocols; and a selector to select an optimal treatment protocol fromsaid plurality of treatment protocols based on the modified systemmodel.

Yet another aspect of the present invention is system for modellingNeutrophil lineage for a general patient, said system comprising aGranulopoiesis system model including a realistic process model forcells involved in Neutrophil production.

Preferably, the system model incorporates a realistic progression ofcells involved in Granulopoiesis disorders including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesisdisorders including Neutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF);

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Preferably, said model is used for recommending an optimal treatmentprotocol, wherein said system further comprises: a plurality oftreatment protocols; and a selector to select an optimal treatmentprotocol from said plurality of treatment protocols based on themodified system model.

Yet another aspect of the present invention is a system for predictingprogression of Granulopoiesis for an individual under a plurality oftreatment protocols, said plurality of protocols including no treatment,said system comprising a Granulopoiesis system model including arealistic process model for cells involved in Neutrophil production; aplurality of treatment protocols; and

a system model modifier. The Neutrophil production system model ismodified by the system model modifier based on parameters specific tothe individual. The system further comprises a predictor that predictsthe progression under the plurality of treatment protocols based on themodified system model.

Preferably, the system model incorporates a realistic progression ofcells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesis andNeutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment-uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Yet another aspect of the present invention is a system for predictingprogression of Granulopoiesis for a general patient under a plurality oftreatment protocols, said plurality of protocols including no treatment,said system comprising a Neutrophil system model including a realisticprocess model for cells involved in Neutrophil production a plurality oftreatment protocols; and a predictor to that predicts the progressionunder the plurality of treatment protocols based on the modified systemmodel.

Still preferably, the system model incorporates a realistic progressionof cells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesis andNeutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Yet another aspect of the present invention is a system for recommendingan optimal treatment protocol for treating cancer using drugs, includingchemotherapy, for an individual, said system comprising a cancer systemmodel a plurality of treatment protocols for treating cancer usingchemotherapy, a system model modifier. The cancer system model ismodified by the system model modifier based on parameters specific tothe individual. The system further comprises a selector to select anoptimal treatment protocol from said plurality of treatment protocolsbased on the modified system model.

Preferably, the system model further comprises a realistic process modelof cancer development; and a realistic treatment model that models theeffects of treating cancer with drugs, including chemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, a set control functions uniquely determine an outcomeof every single step, wherein said control functions depend on age ofcells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytostatic effects, cytotoxic effects, andother effects on cell disintegration of anticancer drugs areincorporated into the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Still preferably, said parameters specific to the individual compriseparameters related to tumor dynamics, patient specific drug PK, anddynamics of dose-limiting host tissues.

Still preferably, said parameters related to tumor dynamics compriseage, weight, gender, percentage of limiting healthy cells, desiredlength of treatment protocol, previous reaction to treatment, molecularmarkers, genetic markers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a system for predictingthe a progression of cancer in individual patients comprising a cancersystem model, a plurality of treatment protocols for treating cancerusing drugs, including chemotherapy a system model modifier. The cancersystem model is modified by the system model modifier based onparameters specific to the individual. The system further comprises apredictor to predict the progression of cancer under the plurality oftreatment protocols based on the modified system model.

Still preferably, the system model further comprises:

a realistic process model of cancer development; and

a realistic treatment model that models the effects of treating cancerwith drugs, including chemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, where a set control functions uniquely determine anoutcome of every single step, wherein said control functions depend onage of cells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytotoxic effects and cytostatic effects ofanticancer drugs are incorporated into the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Still preferably, said parameters specific to the individual compriseparameters related to tumor dynamics, patient specific drug PK, anddynamics of dose-limiting host tissues.

Still preferably, said parameters related to tumor dynamics compriseage, weight, gender, percentage of limiting healthy cells, desiredlength of treatment protocol, previous reaction to treatment, molecularmarkers, genetic markers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a system for predictingthe a progression of cancer in a general patients comprising a cancersystem model, a plurality of treatment protocols for treating cancerusing drugs, including chemotherapy; and a predictor to predict theprogression of cancer under the plurality of treatment protocols basedon the modified system model.

Preferably, the system model further comprises a realistic process modelof cancer development; and a realistic treatment model that models theeffects of treating cancer with drugs, including chemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, where a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, a set control functions uniquely determine an outcomeof every single step, wherein said control functions depend on age ofcells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytotoxic effects and cytostatic effects ofanticancer drugs are incorporated into the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Yet another aspect of the present invention is a method of recommendingan optimal treatment protocol for an individual comprising: creating asystem model; enumerating a plurality of treatment protocols; modifyingthe system model based on parameters specific to the individual; andselecting an optimal treatment protocol from said plurality of treatmentprotocols based on the modified system model.

Preferably, the step of creating the system model further comprises:modelling a biological process; and realistically modelling effects of atreatment on said biological process.

Still preferably, said modelling of biological processes is done by tomathematical modelling biological processes affecting healthy cellpopulations and mathematically modelling biological processes affectingcell populations with at least one disease.

Still preferably, said healthy cell populations include bone-marrowcells and host tissue cells that are affected by said treatment model.

Still preferably, said cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrompocyte cells.

Still preferably, said treatment models comprise treatment specificprocesses that affect cell population.

Still preferably, said treatment specific process is interactionsinvolving at least one of a group comprising pharmacokinetic (PK),pharmacodynamic (PD), cytostatic, cytotoxic, and methods of affectingcell biology and causing cell death, with associated biologicalprocesses.

Still preferably, said parameters specific to the individual include oneor more selected from a group consisting of parameters related to thebiological process' dynamics, patient specific drug PK, PD and dynamicsof dose-limiting host tissues

Still preferably, said parameters related to biological process'dynamics comprise age, weight, gender, blood picture, desired length oftreatment protocol, previous reaction to treatment, molecular markers,genetic markers, pathologic specifics and cytologic specifics.

Still preferably, user-specific parameters are used in selecting theoptimal treatment.

Still preferably, a fitness function is used to perform the selection.

Still preferably, said fitness function incorporates at least oneparameter selected from a group consisting patient survival, time todeath, time to reach a specified disease stage and cure, tumor load,pathogen load, cytotoxicity, side effects, quality of life, cost oftreatment and pain.

Still preferably, a user can input specific coefficients for said atleast one parameter to adjust the fitness function to satisfy the user'sgoals.

Still preferably, the user-specific parameters are based on a user, saiduser being a medical doctor.

Still preferably, the user-specific parameters are based on a user, saiduser being a scientist.

Still preferably, the user-specific parameters are based on a user, saiduser being a drug developer.

Preferably, said selection of treatment protocols incorporate cytotoxiceffects.

Still preferably, said selection of treatment protocols incorporate drugefficacy.

Still preferably, operation research techniques are used in performingthe selection.

Still preferably, heuristics are used to perform searching andselection.

Still preferably, said heuristics comprise computational feasibility.

Still preferably, said recommendation is a combination of disease andtreatment strategy, including type of treatment, device, drug or drugcombination, radiotherapy, surgery and treatment schedule and dosage.

Yet another aspect of the present invention is a method of recommendingan optimal treatment protocol for a general patient comprising: creatinga system model; enumerating a plurality of treatment protocols; andselecting an optimal treatment protocol from said plurality of treatmentprotocols based on the modified system model.

Still preferably, the step of creating the system model furthercomprises: modelling a biological process; and realistically modellingeffects of a treatment on said biological process;

Still preferably, said modelling of biological processes is done bymathematical modelling biological processes affecting healthy cellpopulations and mathematically modelling biological processes affectingcell populations with at least one disease.

Still preferably, said healthy cell populations include bone-marrowcells and host tissue cells that are affected by said treatment model.

Still preferably, said cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrompocyte cells.

Still preferably, said treatment models comprise treatment specificprocesses that affect cell population.

Still preferably, said treatment specific process is interactionsinvolving one of a group comprising pharmacokinetic, pharmacodynamic,cytostatic, cytotoxic, or any other method of affecting cell biology andcausing cell death, with associated biological processes.

Still preferably, user-specific parameters are used in selecting theoptimal treatment.

Still preferably, a fitness function is used to perform the selection.

Still preferably, said fitness function incorporates at least oneparameter selected from a group comprising patient survival, time todeath, time to reach a specified disease stage (including cure)e, tumorload, pathogen load, cytotoxicity, side effects, quality of life, costof treatment and pain.

Still preferably, a user can input specific coefficients for said atleast one parameter to adjust the fitness function to satisfy the user'sgoals.

Still preferably, the user-specific parameters are based on a user, saiduser being a medical doctor.

Still preferably, the user-specific parameters are based on a user, saiduser being a scientist.

Still preferably, the user-specific parameters are based on a user, saiduser being a drug developer.

Still preferably, said selection of treatment protocols incorporatecytotoxic effects.

Still preferably, said selection of treatment protocols incorporate drugefficacy.

Still preferably, operation research techniques are used in performingthe selection.

Still preferably, heuristics are used to perform searching andselection.

Still preferably, said heuristics comprise computational feasibility.

Still preferably, said recommendation is a combination of disease andtreatment strategy, including type of treatment, device, drug, drugcombination, radiotherapy, surgery and treatment schedule and dosage.

Yet another aspect of the present invention is a method of predictingprogression of a biological process in an individual patient under aplurality of treatment protocols, wherein said biological process couldbe related to healthy or diseased processes, said plurality of protocolsincluding no treatment, said method comprising creating a system model,enumerating a plurality of treatment protocols; modifying the systemmodel based on parameters specific to the individual, and selecting anoptimal treatment protocol from said plurality of treatment protocolsbased on the modified system model.

Preferably, the step of creating a system model further comprises:realistically modelling a biological process; and realisticallymodelling the effects of the treatment on said biological process.

Still preferably, said step of modelling a biological process comprisescreating a mathematical model for biological processes affecting healthycell populations and creating a biological processes affecting cellpopulations with at least one disease.

Still preferably, said healthy cell populations include bone-marrowcells and host tissue cells that are affected by said treatment model.

Still preferably, said cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including diseasedNeutrophil cells and diseased Thrombocyte cells.

Still preferably, said treatment models comprise treatment specificprocesses that affect cell population.

Still preferably, said treatment specific process is interactionsinvolving one of a group comprising PK, PD, cytostatic, cytotoxic, orany other method of affecting cell biology and causing cell death, withassociated biological processes.

Still preferably, said parameters specific to the individual include oneor more selected from a group consisting of parameters related to thebiological process' dynamics, patient specific drug PK, PD and dynamicsof dose-limiting host tissues.

Still preferably, said parameters related to biological process'dynamics comprise age, weight, gender, blood picture, desired length oftreatment protocol, previous reaction to treatment, molecular markers,genetic markers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a method of predictingprogression of a biological process in a general patient under aplurality of treatment protocols, wherein said biological process couldbe related to healthy or diseased, said plurality of protocols includingno treatment, said method comprising creating a system model;enumerating a plurality of treatment protocols; and selecting an optimaltreatment protocol from said plurality of treatment protocols based onthe modified system model.

Preferably, the step of creating a system model further comprisesrealistically modelling a biological process; and realisticallymodelling the and the effects of the treatment on said biologicalprocess.

Still preferably, said step of modelling a biological process comprisescreating a mathematical model for biological processes affecting healthycell populations and creating a biological processes affecting cellpopulations with at least one disease.

Still preferably, said healthy cell populations include bone-marrowcells and host tissue cells that are affected by said treatment model.

Still preferably, said cell populations with at least one disease is oneof cancer cells, and diseased bone-marrow cells including at least oneof diseased Neutrophil cells and diseased Thrombocyte cells.

Still preferably, said treatment models comprise treatment specificprocesses that affect cell population.

Still preferably, said treatment specific process is interactionsinvolving one of a group comprising PK, PD, drug cytostatics, drugcytotoxics, and methods of affecting cell biology and causing celldeath, with associated biological processes.

Yet another aspect of the present invention is a method for modellingThrombopietic lineage in an individual, said method comprising:realistically modelling a process to create a process model for cellsinvolved in Thrombopoiesis; and modifying the process model based onparameters specific to the individual.

Preferably, a realistic progression of cells involved in diseasedThrombopoiesis is incorporated in the process model.

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, effects of at least one drug in the realisticprogression of cells involved in Thrombopoiesis is incorporated.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, said process model imitates a course of theindividual's bone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, said process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Preferably, said method is used for recommending an optimum treatmentprotocol, and wherein said method further comprises: enumerating aplurality of treatment protocols; and selecting an optimal treatmentprotocol from said plurality of treatment protocols based on themodified system model.

Yet another aspect of the present invention is a method for modellingThrombopietic lineage in a general patient, said method comprising:realistically modelling a process to create a process model for cellsinvolved in Thrombopoiesis.

Preferably, a realistic progression of cells involved in diseasedthrombopoiesis is incorporated in the process model.

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, effects of at least one drug in the realisticprogression of cells involved in Thrombopoiesis is incorporated.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, said process model imitates a course of theindividual's bone marrow progression, peripheral platelet counts and TPOconcentration changes.

Still preferably, said process model incorporates cell-suppressivetreatment effects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Preferably, said method is used for recommending an optimum treatmentprotocol, and wherein said method further comprises: enumerating aplurality of treatment protocols; and selecting an optimal treatmentprotocol from said plurality of treatment protocols based on themodified system model.

Yet another aspect of the present invention is a method for predictingprogression of Thrombopoiesis and Thrombocytopenia for an individualunder a plurality of treatment protocols, said plurality of protocolsincluding no treatment, said method comprising: creating a realisticmodel of Thrombopoiesis and Thrombocytopenia; generating a plurality oftreatment protocols for affecting Thrombopoiesis and treatingThrombocytopenia using at least one drug;

modifying the model based on parameters specific to the individual; and

predicting the progression of the disease or the natural biologicalprocess under said plurality of treatment protocols based on themodified system model.

Preferably, the model incorporates a realistic progression of cellsinvolved in diseased Thrombopoiesis.

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the model incorporates effects of at least one drug inthe realistic progression of cells involved in Thrombocytopenia.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, the model imitates a course of the individual's bonemarrow progression, peripheral platelet counts and TPO concentrationchanges.

Still preferably, the model incorporates cell-suppressive treatmenteffects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Still preferably, said process model further comprises a plurality ofcompartments.

Still preferably, said compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis are included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the model further incorporates the effects of TPO onthe SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomotisis.

Still preferably, when the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, in the CFU-Meg compartment the cells are sensitive toTPO concentration regardless of the concentration of TPO.

Still preferably, the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, in the SC compartment when the TPO concentration isabove the threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably, in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, the platelet releasing cells contribute platelets tothe first sub-compartment of the PL compartment.

Yet another aspect of the present invention is a method for predictingprogression of Thrombopoiesis and Thrombocytopenia for a general patientunder a plurality of treatment protocols, said plurality of protocolsincluding no treatment, said method comprising: creating a realisticmodel Thrombopoiesis and Thrombocytopenia; generating a plurality oftreatment protocols for affecting Thrombopoiesis and treatingThrombocytopenia using at least one drug; and predicting the progressionof the disease or the natural biological process under said plurality oftreatment protocols based on the modified system model.

Preferably, the model incorporates a realistic progression of cellsinvolved in diseased Thrombopoiesis.

Still preferably, diseased Thrombopoiesis includes Thrombocytopenia.

Still preferably, the model incorporates effects of at least one drug inthe realistic progression of cells involved in Thrombocytopenia.

Still preferably, said at least one drug is Thrombopoietin (TPO).

Still preferably, the model imitates a course of the individual's bonemarrow progression, peripheral platelet counts and TPO concentrationchanges.

Still preferably, the model incorporates cell-suppressive treatmenteffects and administration of TPO to the patient.

Still preferably, said cell-suppressive treatment is chemotherapy.

Still preferably, said process model further comprises a plurality ofcompartments.

Still preferably, said compartments include:

a stem cell (SC) compartment that comprises bone marrow haemopoieticprogenitors that have an ability to differentiate into more than onecell line wherein cells in the stem cell compartment proliferate anddifferentiate into one of megakaryocyte;

a colony forming units-megakaryocytes (CFU-Meg) compartment, wherein themegakaryocyte progenitors get committed as a megakaryocyte line andspend some time multiplying and maturing;

a megakaryoblast (MKB) compartment, which receives the cells fromCFU-Meg, wherein the cells in the MKB compartment have lost theirability to proliferate but are not mature to release platelets;

a MK16 compartment, which receives cell from the MKB compartment,wherein a subset of cells in the MK16 compartment release platelets at aconstant rate until they exhaust their capacity and are disintegratedand a second subset of cells do not release platelets but continue withendomitosis;

a MK32 compartment that receives cells from the MK16 compartment,wherein a subset of cells in this compartment release platelets and asecond subset of cells do not release platelets but continue withendomitosis;

a MK64 compartment that receives cells from the MK32 compartment whereina subset of cells in this compartment release platelets and a secondsubset of cells do not release platelets but continue with endomitosis;

a MK128 compartment that receives cells from the MK64 compartmentwherein a subset of cells in this compartment release platelets; and

a platelets (PL) compartment.

Still preferably, an effect of apoptosis are included with an overalleffect of cell proliferation in giving rise to an amplification of cellnumbers in a corresponding compartment.

Still preferably, the model further incorporates the effects of TPO onthe SC, CFU-Meg and MKB compartments.

Still preferably, the effects are expressed in terms of effects of TPOconcentration on amplification rate, rate of cell maturation and afraction of cells that undergo endomotisis.

Still preferably, when the TPO concentration is above a predeterminedthreshold level, the amplification rate of cells in the SC compartmentare affected and below the threshold the amplification rate is dependentonly on a current number of cells.

Still preferably, in the CFU-Meg compartment the cells are sensitive toTPO concentration regardless of the concentration of TPO.

Still preferably, the transit time is same in all platelet releasingcompartments and the transit time of the SC, CFU-Meg and MKBcompartments are functions of micro-environmental conditions.

Still preferably, in the SC compartment when the TPO concentration isabove the threshold, the transit time is shortened based the dose.

Still preferably, in the CFU-Meg and MKB, the transit time is solelybased on TPO concentration.

Still preferably, a fraction of cells in the SC compartment that commitsto megakaryocytic lineage is constant and dependent on TPO.

Still preferably, in the CFU-Meg and MKB compartments, every mature cellpasses on to the next compartment.

Still preferably, in the MK16, MK32 and MK64 compartments, a fraction ofcells pass on to the next compartment, said fraction being dependent onthe TPO concentration.

Still preferably, cells from MK128 compartment do not flow into anyother compartment.

Still preferably, each of said compartments is further divided intosub-compartments, each of said sub-compartments containing cells of aspecific age in hours.

Still preferably, cells that spend all their corresponding transit timein a given compartment pass on to the next compartment, wherein cellsthat have left a corresponding compartment each hour fill the firstsub-compartment of the next compartment.

Still preferably, the platelet releasing cells contribute platelets tothe first sub-compartment of the PL compartment.

Yet another aspect of the present invention is a method for modellingNeutrophil lineage for an individual, said method comprising: creating arealistic a Neutrophil system model including a realistic process modelfor cells involved in Neutrophil lineage; and modifying the system modelbased on parameters specific to the individual.

Preferably, the system model incorporates a realistic progression ofcells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system model incorporates effects of at least onedrug in the realistic progression of cells involved in Granulopoiesisand Neutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said system model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters of the system.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided into issubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Preferably, said method is used for recommending an optimum treatmentprotocol, and wherein said method further comprises: enumerating aplurality of treatment protocols; and selecting an optimal treatmentprotocol from said plurality of treatment protocols based on themodified system model.

Yet another aspect of the present invention is a method for modellingNeutrophil lineage for a general patient, said method comprising:creating a realistic a Granulopoiesis system model including a realisticprocess model for cells involved in Granulopoiesis lineage.

Preferably the system model incorporates a realistic progression ofcells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system model incorporates effects of at least onedrug in the realistic progression of cells involved Granulopoiesis andin Neutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said system model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Preferably, wherein said model comprises a mitotic compartment, and apost mitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Still preferably, said method is used for recommending an optimumtreatment protocol, and wherein said method further comprises:enumerating a plurality of treatment protocols; and selecting an optimaltreatment protocol from said plurality of treatment protocols based onthe modified system model.

Yet another aspect of the present invention is a method for predictingprogression of Granulopoiesis for an individual under a plurality oftreatment protocols, said plurality of protocols including no treatment,said system comprising: creating a Neutrophil system model including arealistic process model for cells involved in Neutrophil production;generating a plurality of treatment protocols; modifying the systemmodel modifier, wherein said Neutrophil system model is modified by thesystem model modifier based on parameters specific to the individual;and predicting the progression under the plurality of treatmentprotocols based on the modified system model.

Preferably, the system model incorporates a realistic progression ofcells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesis andNeutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment are tomodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Yet another aspect of the present invention is a method for predictingprogression of Granulopoiesis for a general patient under a plurality oftreatment protocols, said plurality of protocols including no treatment,said system comprising: creating a Neutrophil system model including arealistic process model for cells involved in Neutrophil production;generating a plurality of treatment protocols; and predicting theprogression under the plurality of treatment protocols based on themodified system model.

Still preferably, the system model incorporates a realistic progressionof cells involved in Granulopoietic disorders, including Neutropenia.

Still preferably, the system incorporates effects of at least one drugin the realistic progression of cells involved in Granulopoiesis andNeutropenia.

Still preferably, said at least one drug is Granulocyte ColonyStimulating Factor (G-CSF).

Still preferably, said model comprises at least three stages,

a first stage related to an administered amount of cytokine;

a second stage representing a pharmacokinetic behavior of G-CSF; and

a third stage representing a pharmacodynamic effect of G-CSF on kineticparameters.

Still preferably, said model comprises a mitotic compartment, and a postmitotic compartment, said mitotic compartment being divided intosubcompartments wherein a kth sub-compartment contains cells of agebetween k−1 and k hours relative to a time of entry into the mitoticcompartment.

Still preferably, effects of toxic drugs, including chemotherapy areincorporated by mapping various cell-cycle phases to thesub-compartments and formulating a function of cytotoxic effects oftoxic drugs, including chemotherapy on the cell-cycle phases.

Still preferably, the effects of G-CSF on the mitotic compartment aremodeled as an increase in a rate of cells entering the myeloblastscompartment from an uncommitted stem cell pool.

Still preferably, the post-mitotic compartment is modeled as a singlepool of cells wherein cells in a last sub-compartment of the mitoticcompartment enters the post-mitotic compartment and a proportion ofcells within the post-mitotic compartment enters the mature Neutrophilpool every hour.

Still preferably, effects of G-CSF on the Neutrophil lineage are modeledas a decrease in the cells in the post-mitotic compartment which issubsequently compensated by an increased production in the mitoticcompartment, said compensation sustaining an increase in Neutrophilcount.

Still preferably, an elimination of Neutrophils in the post-mitoticcompartment is represented by a Poisson distribution.

Still preferably, the cytotoxic effects of toxic drugs, includingchemotherapy in the post-mitotic compartment is modeled as an effect ona single pool of cells.

Still preferably, kinetic of G-CSF is modeled as an exponentialdistribution.

Still preferably, a selection of an optimal treatment uses an objectivefunction that aims at minimizing G-CSF administration and returningNeutrophil lineage to normal levels.

Still preferably, said selection is performed using linear programming.

Still preferably, pharmacokinetics and pharmacodynamics of G-CSF aredefined using piecewise linear functions.

Yet another aspect of the present invention a method for recommending anoptimal treatment protocol for treating cancer using drugs, includingchemotherapy, for an individual, said method comprising: creating acancer system model; enumerating a plurality of treatment protocols fortreating cancer using drugs, including chemotherapy; modifying thesystem model based on parameters specific to the individual; andselecting an optimal treatment protocol from said plurality of treatmentprotocols based on the modified system model.

Preferably, the system model further comprises: a realistic processmodel of cancer development; and a realistic treatment model that modelsthe effects of treating cancer with drugs, including chemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, where a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, a set of control functions uniquely determine anoutcome of every single step, wherein said control functions depend onage of cells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytotoxic effects, cytostatic effects andother effects on cell disintegration of anticancer drugs areincorporated into the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Still preferably, said parameters specific to the individual compriseparameters related to tumor dynamics, patient specific drug PK, anddynamics of dose-limiting host tissues.

Still preferably, said parameters related to tumor dynamics compriseage, weight, gender, percentage of limiting healthy cells, desiredlength of treatment protocol, previous reaction to treatment, molecularmarkers, genetic markers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a method of predicting aprogression of cancer in an individual, said method comprising: creatinga cancer system model; enumerating a plurality of treatment protocolsfor treating cancer using drugs, including chemotherapy; modifying thesystem model based on parameters specific to the individual; andselecting an optimal treatment protocol from said plurality of treatmentprotocols based on the modified system model.

Preferably, the system model further comprises: a realistic processmodel of cancer development; and a realistic treatment model that modelsthe effects of treating cancer with drugs, including chemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, a set control functions uniquely determine an outcomeof every single step, wherein said control functions depend on age ofcells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytotoxic and other cell disintegrationeffects, and cytostatic effects of anticancer drugs are incorporatedinto the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Still preferably, said parameters specific to the individual compriseparameters related to tumor dynamics, patient specific drug PK, anddynamics of dose-limiting host tissues.

Still preferably, said parameters related to tumor dynamics compriseage, weight, gender, percentage of limiting healthy cells, desiredlength of treatment protocol, previous reaction to treatment, molecularmarkers, genetic markers, pathologic specifics and cytologic specifics.

Yet another aspect of the present invention is a method of predicting aprogression of cancer in a general patient, said method comprising:creating a cancer system model; enumerating a plurality of treatmentprotocols for treating cancer using drugs, including chemotherapy; andselecting an optimal treatment protocol from said plurality of treatmentprotocols based on the modified system model.

Still preferably, the system model further comprises: a realisticprocess model of cancer development; and a realistic treatment modelthat models the effects of treating cancer with drugs, includingchemotherapy.

Still preferably, said process model incorporates a distribution ofcycling cells and quiescent cells.

Still preferably, a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.

Still preferably, the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsubcompartment using stepwise equations.

Still preferably, a probability vector is used to determine a fractionof cells that leaves any subcompartment in a compartment to move to afirst subcompartment of the next compartment.

Still preferably, a set control functions uniquely determine an outcomeof every single step, wherein said control functions depend on age ofcells, state of a current population and associated environment.

Still preferably, a tumor is modelled as a combination of a plurality ofhomogeneous group of cells, each of said homogeneous group of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.

Still preferably, in each step, a number of cells in eachsub-compartment of each compartment of each group is calculatedaccording to factors including a previous state, parameters of tumor,tumor current microenvironment and drug concentration.

Still preferably, spatial structure of the tumor is included in themodel.

Still preferably, PK and PD, cytotoxic effects and cytostatic effects ofanticancer drugs are incorporated into the model.

Still preferably, a dose-limiting toxicity is incorporated into themodel.

Yet another aspect of the present invention is a computer programproduct, including a computer readable medium, said program productcomprising a set of instruction to enable a computer system to aid inrecommending an optimal treatment protocol for an individual comprising:

a system model code; treatment protocol code for a plurality oftreatment protocols;

a system model modifier code, wherein said system model is modified bythe system model modifier based on parameters specific to theindividual; and

a selector code to select an optimal treatment protocol from saidplurality of treatment protocols based on the modified system model.

Preferably, the system model code further comprises: a realisticbiological process model code; and a realistic treatment model code thatenables a computer to model the effects of a treatment on the biologicalprocess.

Yet another aspect of the present invention is a computer programproduct, including a computer readable medium, said program productcomprising a set of instructions to enable a computer system to aid inrecommending an optimal treatment protocol for a general patientcomprising: a system model code; treatment protocol code for a pluralityof treatment protocols; and a selector code to select an optimaltreatment protocol from said plurality of treatment protocols based onthe modified system model.

Preferably, the system model code further comprises: a realisticbiological process model code; and

a realistic treatment model code that enables a computer to model theeffects of a treatment on the biological process.

III. BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be understood and appreciated more fully fromthe following detailed description taken in conjunction with theappended drawings in which:

FIG. 1 is a schematic illustration of the basis of the presentinvention;

FIGS. 2A and B are diagram charts illustrating steps of the invention,useful in understanding FIG. 1; FIG. 2A further illustrates a protocolspace;

FIG. 3 is a schematic illustration of a biological model, in accordancewith one embodiment of the present invention;

FIG. 4 is a chart illustration of the biological model of FIG. 3;

FIG. 5 is a graphical illustration of the chart of FIG. 4;

FIG. 6 is a chart illustration of the biological model of FIG. 3 in adifferent format;

FIG. 7 is a graphical illustration of the chart of FIG. 6;

FIGS. 8A and 8B are graphical illustrations of the output of the modelof FIG. 3;

FIGS. 9A and 9B are graphical illustrations of experimental data ascompared to the output shown in FIGS. 8A and 8B;

FIG. 10 is a schematic illustration of a biological model, in accordancewith a further embodiment of the present invention;

FIG. 11 is a graphical illustration of results of the simulation of themodel shown in FIG. 10;

FIGS. 12A and 12B are graphical illustrations of the effects of twodoses of G-CSF on the Neutrophil line, according to the model of FIG.10;

FIG. 13 is a schematic illustration of a biological model, in accordancewith a further embodiment of the present invention;

FIGS. 14 and 15 show a comparison of Neutrophil production according tothe described model and experimental data in the literature.

IV. DETAILED DESCRIPTION OF THE PRESENT INVENTION

Systems and methods have been disclosed for identifying optimaltreatment strategies for a general patient and a specific individualpatient, and for predicting progression of a biological process andtreatment, using selected parameters. The techniques are based onbiological and clinical knowledge, mathematical models, computersimulations, and optimization methods. The optimization techniques couldbe any available mathematical techniques including, but not limited to,linear programming and heuristic search. The disclosed heuristic searchtechniques use heuristic (or rules of thumb) determinations.

Such a use of heuristics search enables the user to find near optimalsolutions even for complex mathematical descriptions of a combination ofrelevant biological, clinical, pharmacological scenarios. These complexmathematical descriptions are contemplated to be realistic simulationsof actual scenarios. It is contemplated that this holds both for thegeneral case (“optimal generic treatment”), as well as at the level ofan individual patient.

The general case is intended for several purposes including use bypharmaceutical companies and by researches who are more concerned withdesigning systems and recommending treatment for a general patient asopposed to recommending treatment for a specific patient in a clinicalsetting. It is also contemplated that the general case can be used for abetter understanding of the underlying processes for any other use.Likewise, the individual case is intended for several purposesincluding, for example, the use by a doctor to understand the progressof a treatment protocol or the progression of a disease, and to optimizethe treatment for a specific individual patient. These indicated usesare not intended to be restrictive. It should be clear to the skilledpractitioner that the techniques disclosed can be put to several otheruses.

FIG. 1 illustrates the general concept behind the disclosed technique.Detailed parameters are input to a protocol space. The protocol spacecomprises a plurality of treatment protocols. From this protocol spacean optimal treatment protocol is selected by performing a heuristicsearch.

FIG. 2 shows a diagram chart that depicts an illustration of anembodiment of the disclosed techniques for optimization. The Figuregenerally depicts the basic concept. The disclosed techniques are usedto optimize a drug delivery protocol after consideration of a pluralityof possible protocols. The plurality of protocols together form aprotocol space 2.5. Determination of an optimal protocol is partiallybased on specific parameters input by a user. The user may be aphysician, a drug developer, a scientist, or anyone else who may need todetermine a treatment strategy,

needs of a specific user and other particulars such as patient survival,efficacy, time to death, time to reach a specified disease stage(including cure), tumor load, pathogen load, cytotoxicity, side effects,quality of life, cost of treatment, and pain. maximum length oftreatment, confidence level, etc. In case of the disclosed techniquesfor the individual patient, general characteristic parameters whichdetermine the system's behaviour, are altered according to individualpatient characteristics and/or medical history of the patient.

Initially, system models are created. These included models to simulateall the relevant biological, clinical and pharmaceutical process 2.1.These models include mathematical models for processes that affecthealthy cells as well as mathematical models for processes that affectcell populations with one or more diseases. In addition, a model oftreatment effects 2.3 on each of these processes is created. Thetreatment effects include processes that are specific to individualtreatment. Such a treatment may be based on the effects of a drug'sprocess that affects the relevant cell population. Examples of theseeffects include interactions involving pharmacokinetic (PK),pharmacodynamics (PD), cytotoxic and cytostatics, or any other method ofaffecting cell biology and causing cell death, with associatedbiological processes.

The combination of these models provides a detailed mathematical modelof the overall bio-clinical scenario in a general sense or for aspecific patient, together with the specific effects of a particulartreatment. Once the comprehensive model is constructed, thecharacteristic parameters are incorporated in it. The characteristicparameters could be either population averaged or patient specific. Incase of the

parameters could be either population averaged or patient specific. Incase of the general case, average patient parameters are incorporated.The average patient parameters include parameters related to biologicalprocess dynamics, average drug PK, average drug PD and dynamics ofdoes-limiting host tissues. In this way a “virtual general patient” inthe form of a complete detailed model 2.4 is generated.In case of the individual case, patient specific parameters 2.2 areincorporated. The patient specific parameters include parameters relatedto biological process dynamics, patient specific drug PK, patientspecific drug PD and dynamics of does-limiting host tissues. Theparameters related to biological process dynamics include, age, gender,weight, blood picture, desired length of the treatment protocol,previous reactions to treatment, molecular markers, genetic markers,pathologic specifics and cytologic specifics or clinical indications. Inthis way a “virtual individual patient” in the form of a completedetailed model 2.4 is generated.

Then a protocol space 2.5 is generated. To do this, possiblepermutations of certain parameters such as drug doses, dosing intervals,etc. are considered. Thus, a number of possible treatment protocols isgenerated. This number could be very large because of the number ofpermutations possible. The amount of possibilities depends on the numberand ranges of parameters considered.

A fitness function 2.6 is then constructed by mathematically consideringdifferent possible factors which may be influenced by the treatment.These may include patient survival, time to death, time to reach aspecified disease stage (including cure), tumor load, pathogen load,cytotoxicity to normal or diseased tissues, other side effects, qualityof life, cost of treatment, pain, etc.

The user can alter certain specific parameters in the fitness functionso as to adjust this function to the user's specific goals. The user canbe anybody, including a medical doctor, a scientist or a drug developer.Based on the selected parameters, the fitness function is applied. Thisresults in the calculation of a fitness score for each and everyprotocol in the protocol space. Finally, the optimization step iscarried out 2.7, either by search heuristics or by analytical methods,in order to select the optimal treatment protocol 2.8 from all thescored possibilities. The analytical methods include the use ofOperations Research techniques. In selecting the optimal treatmentprotocol cytotoxic effects as well as treatment efficacy areincorporated, as well as other objectives of the said fitness function.The heuristics, or rules of thumb employed include computationalfacility. The optimal treatment protocol is a combination of disease andtreatment strategy, including type of treatment, device, drug or drugcombination, radiotherapy, surgery and treatment schedule.

In this way, a disease specific, patient specific, situation specific,treatment type specific (e.g. drug therapy, operation, radiotherapy),drug specific, or an objective specific treatment protocol may beobtained. The actual time it takes once the parameters are entered maybe negligibly short or up to hours, depending on the length of thesimulated treatment period and the power of the specific searchheuristics and the computational tools, making this a very feasibletool.

Systems and methods embodying the above disclosed technique for ageneral patient as well as for an individual patient are within thescope of the present invention.

The system can be implemented remotely over a distributed computingsystem with the user remotely dialing in. It can also be implementedover the internet. The computer could be a PC, mainframe, a workstationor a remote computer on a network.

Another aspect of the disclosed technique is a computer program code.The computer program product includes a computer readable medium. Itshould be noted that the computer readable medium includes any fixedmedia including, but not limited to, floppy disk, hard disk, CD, chips,tapes, cartridges with Ics, etc. The computer readable media alsoincludes instructions transmitted through a network or downloaded fromthe Internet. The computer program product includes instructions forenabling a computer to aid in selecting a treatment protocol. Theinstructions include a system model code. A treatment protocol code isprovided for a plurality of treatment protocols. In case of thedisclosed technique for an individual patient, a system model modifiercode is provided that enables the computer to modify the system modelbased on parameters specific to the individual. A selector code enablesa computer to select an optimal treatment protocol from the plurality oftreatment protocols based on the modified system model.

Construction of detailed mathematical models for biological processesand treatments are discussed herein in relation to various otherembodiments of the disclosed technique. Techniques involving a model ofplatelets production and related diseases, including Thrombocytopenia,with treatment by TPO, a model of Neutrophil production and relateddiseases, including Neutropenia, and treatment by G-CSF, and a model ofcancer growth and cancer treatment, including chemotherapy, aredisclosed herein. An embodiment for specific optimization (by linearprogramming) is implemented for the system involving the Neutrophilmodel. An embodiment that uses a general heuristic optimization methodis disclosed as well.

IV.A. Thrombopoiesis and Thrombopoietin (TPO)

An embodiment of the present invention involves the disclosed techniquesfor modeling the Thrombopietic lineage, diseased Thrombopoiesis such asThrombocytopenia and treatment with Thrombopoietin. Thrombocytopenia isa common hazardous blood condition, which may appear in differentclinical situations, including cancer chemotherapy. Recently, aThrombopoiesis-controlling cytokine, Thrombopoietin (TPO), was isolatedand its human recombinant analog became available. A mathematical modelis disclosed herein that simulated dynamics of a Thrombopoietic lineagein the bone marrow, of platelet counts in the periphery, and effects ofTPO administration on the lineage and platelet counts.

TPO is a cytokine, glycoprotein of about 350 amino acids, that resembleserythropoiesis-stimulating hormone, erythropoietin. Its syntheticanalogs, recombinant human Thrombopoietin (rHuTPO) and recombinant humanmegakaryocyte growth and development factor (rHuMGDF), are available aswell and are undergoing clinical trials.

For further details see Alexander W S: Thrombopoietin. Growth Factors.1999; 17(1); pp. 13-24; Kaushansky K: Thrombopoietin: the primaryregulator of platelet production. Blood. July 1995; Vol. 86(2); pp.419-431; Vadhan_Raj-Raj S: Recombinant human Thrombopoietin: clinicalexperience and in vivo biology. Seminars Hem. July 1998; Vol. 35(3); pp.261-268; Harker L A: Physiology and clinical applications of plateletgrowth factors. Current Opinion Haematol. 1999; Vol. 6; pp. 127-134; andNeelis K J, Hartong S C, Egeland T, Thomas G R, Eaton D L, Wagemaker G:The efficacy of single-dose administration of Thrombopoietin withcoadministration of either Granulocyte/macrophage or Granulocytecolony-stimulating factor in myelosuppressed rhesus monkeys. Blood.October 1997; Vol. 90(7); pp. 2565-2573.

These compounds have been shown to have the same biological activity asTPO has, so the term TPO will be used without distinguishing between itsdifferent forms and analogs.

TPO is a primary growth factor of the Thrombopoietic cell line both invivo and in vitro. Aside from this, TPO may be potent in stimulation andco-stimulation of other haemopoietic lineages (e.g., Granulopoietic orerythropoietic).

IV.A.1. Model of the Biological System

a) Background of Thrombopoiesis

Like all other haemopoietic lines, the Thrombopoietic line originatesfrom poorly differentiated, multipotential cells, that are capable ofsome division and self-reconstitution. For more background details, seeSwinburne J L, Mackey M C: Cyclical Thrombocytopenia: characterizationby spectral analysis and a review. J Theor Medicine. 2000; Vol. 2; pp.81-91; and Beutler E, Lichtman M A, Coller B S, Kipps T J: WilliamsHAEMATOLOGY. 5^(th) edition McGraw-Hill, Inc. 1995; Chapter 118; pp.1149-1161. Such bone marrow cell compartments as pluripotentialhaemopoietic stem cells and common myeloid progenitor cells (CFU-GEMM)have more or less these characteristics. For more background details,see Beutler E, Lichtman M A, Coller B S, Kipps T J: WilliamsHAEMATOLOGY. 5^(th) edition McGraw-Hill, Inc. 1995; Chapter 118; pp.1149-1161.

Gradually, the cells become more and more differentiated and thuscommitted to the Thrombopoietic line. At this stage they proliferateextensively. Colony-forming Units-megakaryocytes (CFU-Meg) is an exampleof such compartment. Sometimes burst-forming units-megakaryocyte(BFU-Meg), promegakaryoblasts or megakaryoblasts are considered ashaving the similar properties. For more background details, seeSwinburne J L, Mackey M C: Cyclical Thrombocytopenia: characterizationby spectral analysis and a review. J Theor Medicine. 2000; Vol. 2; pp.81-91; and Beutler E, Lichtman M A, Coller B S, Kipps T J: WilliamsHAEMATOLOGY. 5^(th) edition McGraw-Hill, Inc. 1995; Chapter 118; pp.1149-1161.

The committed megakaryocytopoietic cells, megakaryocyte precursors, gothrough several stages of maturation. However, megakaryocyte maturationis somewhat different from that of other haemopoietic lines. Here, alongwith cytoplasmic maturation, cell nuclei undergo mitotic events.However, although the DNA material of these cells doubles, cell divisiondoes not happen. Such incomplete mitosis is termed endomitosis orendoreduplication. Consequently, the cell becomes poliploid with 2N, 4N,8N, etc., amount of DNA. Some authors call the cells with 2N to 4Nchromosome number promegakaryoblasts, others call them megakaryoblastsor immature megakaryocytes. For more background details, see Swinburne JL, Mackey M C: Cyclical Thrombocytopenia: characterization by spectralanalysis and a review. J Theor Medicine. 2000; Vol. 2; pp. 81-91; andBeutler E, Lichtman M A, Coller B S, Kipps T J: Williams HAEMATOLOGY.5^(th) edition McGraw-Hill, Inc. 1995; Chapter 118; pp. 1149-1161.

Usually, megakaryocytes do not start to release platelets until theyreach 8N to 16N state. For more background details, see Gordon A S:Regulation of haematopoiesis. N.Y. 1970 Vol. 2, Section IX (textbook);and Beutler E, Lichtman M A, Coller B S, Kipps T J: WilliamsHAEMATOLOGY. 5^(th) edition McGraw-Hill, Inc. 1995; Chapter 118; pp.1149-1161.

Then they begin to create demarcation membranes that envelop cytoplasmfragments generating platelets. The platelets are released into theblood stream. A small fraction of the megakaryocytes do not cease theirendoreduplication at the 16N-stage, but rather continue with one or moreadditional endomitoses and get thus a ploidy of 32N or more. Forbackground details, see Swinburne J L, Mackey M C: CyclicalThrombocytopenia: characterization by spectral analysis and a review. JTheor Medicine. 2000; Vol. 2; pp. 81-91.

The amounts of cytoplasm, cell volume and the ability to releaseplatelets increase proportionally to the cell ploidy. For backgrounddetails, see Harker L A, Finch C A: Thrombokinetics in man. J ClinInvest. 1969; Vol. 48; pp. 963-974; and Harker L A: Thrombokinetics inidiopathic Thrombocytopenic purpura. Br J Haematol. 1970; Vol. 19; pp.95-104.

b) B. Mathematical Model

Reference is now made to FIG. 3, which is a detailed illustration of amodel predicting Thrombopoiesis. As shown in FIG. 3, the Thrombopoieticlineage is divided into eight compartments. The first compartment,called Stem Cells (SC) and labeled 30, refers to all bone marrowhaemopoietic progenitors that have an ability to differentiate into morethan one line (e.g., pluripotential stem cells, CFU-GEMM, and others).Cells of SC compartment 30 proliferate, giving rise to “new” stem cells,or mature, and subsequently differentiate into megakaryocytes or otherprecursors. Although the consideration of the former process, i.e. therenewal of the stem cells by “new” ones, is not completely understoodbiologically, our simple description may serve as an acceptableassumption since the characteristics of this population are notelaborated in details. For background details, see, Schofield R, Lord BI et al: Self-maintenance capacity of CFU-S. J Cellular Phisiol. 1980;Vol. 103: 355-362; and Rosendaal M, Hodgson G S, Bradley T R:Organization of haemopoietic stem cells: the generation-age hypothesis.Cell Tissue Kinetics. 1979; Vol. 12: 17-29.

Cell death through apoptosis may have a significant effect on cellnumber within proliferating compartments. For background details, see,Swinburne J L, Mackey M C: Cyclical Thrombocytopenia: characterizationby spectral analysis and a review. J Theor Medicine. 2000; Vol. 2; pp.81-91.

However, the effect of apoptosis is combined, with the effect of cellproliferation into a total amplification of cell number in a givencompartment (for example α_(SC)). An assumption is made that noapoptosis occurs in non-proliferating megakaryocytic compartments, dueto lack of evidence to the contrary. However, an assumption of apoptoticnon-proliferating megakaryocytes can be incorporated in the mathematicalmodel.

Biologically, rates of proliferation and maturation, the ability toreconstitute, and other characteristics differ between particular celltypes within a primitive progenitor population. However, in this modelthere is no distinction between them; all progenitor cells areconsidered to be one population with common properties.

It has been shown conventionally that probabilities of stem celldifferentiation into one or another haemopoietic lineage are constant intime. Thus, it is assumed here that a flow of stem cells into themegakaryocyte lineage is fixed (for example Φ_(SC)). For backgrounddetails, see Mayani H, Dragowska W, Lansdorp P M: Lineage commitment inhuman hemopoiesis involves asymmetric cell division of multipotentprogenitors and does not appear to be influenced by cytokines. JCellular Physiol. 1993; Vol. 157; pp. 579-580; Golde D W: The Stem Cell.Medicine. December 1991; Morrison 53, Uchida N, Weissman I L: Thebiology of haematopoietic stem cells. Annu Rev Cell Dev Biol. 1995; Vol.11; pp. 35-71; and von Schulthess G K, Gessner U: Oscillating plateletcounts in healthy individuals: experimental investigation andquantitative evaluation of Thrombopoietic feedback control. Scand JHaematol. 1986; Vol. 36; pp. 473-479.

The same was assumed about the stem cell self-renewal. Thus, after thecells spend a defined transit time, for example τ_(SC), in SCcompartment 30, a certain constant fraction of the cells return to their“young state”, i.e. start their passage through SC compartment 30 again,as shown in line 31. Another constant fraction (Φ_(SC), for example) ofcells pass into the next compartment named Colony-Forming Units(CFU-Meg), labeled 40. It is presumed that remaining stem cellsdifferentiate into haematopoietic lineages other than megakaryocytic.

CFU-Meg refers to all cells that are already committed to themegakaryocyte line but are still capable of proliferation. Cells ofCFU-Meg compartment 40, like those of SC compartment 30, spend some timemultiplying at an amplification rate of about α_(SFU), for example, andmaturing before losing their proliferative abilities and passing on tothe next compartment 50, called megakaryoblasts (MKB). For backgrounddetails see, Eller J, Gyori I et al: Modelling Thrombopoiesisregulation—I: model description and simulation results. Comput MathApplic. 1987; Vol. 14 (9-12); pp. 841-848.

The time they spent in CFU-Meg compartment is τ_(CFU).

MKB compartment 50 includes all the cells that have lost the ability toproliferate, but are not yet sufficiently mature to release platelets.For the purposes of the model, the assumption is made thatmegakaryocytes do not start to release platelets until they reach the16N-ploidy phase. For background details, see Gordon A S: Regulation ofhaematopoiesis. N.Y. 1970 Vol. 2, Section IX (textbook).

Hence, MKB refers to 2N, 4N and 8N cells of megakaryocyte lineage thatcannot divide, at all stages of cytoplasmic maturity. After these cellsspend the designated transit time τ_(MKB), for example, in MKBcompartment 50, they move to the next compartment 60, which is a MK16bone marrow compartment.

The cells of MK16 compartment 60 are megakaryocytes of 16N-ploidy classthat release platelets at a constant uniform rate (γ_(MK16)) until theyexhaust their capacity (C_(MK16), for example), and then aredisintegrated. For background details, see, Harker L A, Finch C A:Thrombokinetics in man. J Clin Invest. 1969; Vol. 48; pp. 963-974; andEller J, Gyori I et al: Modelling Thrombopoiesis regulation—I: modeldescription and simulation results. Comput Math Applic. 1987; Vol. 14(9-12); pp. 841-848.

Cell volume has a linear relationship with megakaryocyte ploidy. Hence,it is assumed that all 16N-megakaryocytes have the same volume and,thus, the same platelet-releasing capacity. For background details, see,Harker L A, Finch C A: Thrombokinetics in man. J Clin Invest. 1969; Vol.48; pp. 963-974.

Therefore all platelet-releasing 16N-megakaryocytes are in transit forthe same amount of time (τ_(MK16), for example) until they are exhaustedand disintegrated.

However, some 16N-megakaryocytes do not participate in platelet release,but rather continue with another endomitosis over a 48-hour time period,and become 32N-megakaryocytes. These constitute a new and distinct MK32compartment 70. Thus, after time μ in MK16 compartment 60, a certainfraction of the cells leave MK16 compartment 60 and go on to MK32compartment 70.

32N-megakaryocytes release platelets as well. The rate of plateletrelease is constant for every compartment and proportional to the ploidystate of megakaryocytes in it. For background details, see, Harker L A,Finch C A: Thrombokinetics in man. J Clin Invest. 1969; Vol. 48; pp.963-974; and Harker L A: Thrombokinetics in idiopathic Thrombocytopenicpurpura. Br J Haematol. 1970; Vol. 19; pp. 95-104.

Thus, every 16N-megakaryocyte releases, for example, γ_(MK16) plateletsper hour and every 32N-megakaryocyte, for example, releases γ_(MK32)platelets per hour (twice as much). However, 32N-megakaryocytes are notexhausted more quickly than 16N-megakaryocytes, since they have 2 timesgreater volume and platelet-releasing capacity. Consequently, allplatelet-releasing megakaryocyte compartments have the same transittime.

Once again, some fraction of cells, for example Φ_(MK32), are notengaged in platelet formation, and continue to the 64N-stage. Additionalendomitosis in MK32 compartment 70 takes the same amount of time μ as inMK16 compartment 60. The 64N-megakaryocytes continue the process in anew MK64 compartment 80, and Φ_(MK64) of them become 128N-cells in yetanother MK128 compartment 90. Additional endomitosis in MK64 compartment80 takes the same amount of time μ as before. Megakaryocytes of greaterploidy classes have not been known to be encountered in humans.

Finally, there is a platelet (PL) compartment 100. This is not a bonemarrow compartment, but rather the platelet pool in the peripheral bloodPlatelets released from megakaryocytes of 16N-, 32N-, 64N-, and128N-ploidy classes enter platelet compartment 100. There are twomechanisms of platelet elimination from circulation: By age-dependentdestruction and by the normal utilization in order to maintain theintegrity of blood vessels. For background details, see, Harker L A,Roskos L K, Marzec U M, Carter R A, Cherry J K, Sundell B, Cheung E N,Terry D, Sheridan W: Effects of megakaryocyte growth and developmentfactor on platelet production, platelet life span, and platelet functionin healthy human volunteers. Blood. 2000 April; Vol. 95(8); pp.2514-2522; and von Schulthess G K, Gessner U: Oscillating plateletcounts in healthy individuals: experimental investigation andquantitative evaluation of Thrombopoietic feedback control. Scand JHaematol. 1986; Vol. 36; pp. 473-479.

The first mechanism is reflected as platelet disappearance after theyspend their designated transit time, for example, in the PL compartment.The second one is rather age-independent and it is reflected as constantplatelet efflux (d) throughout all platelet age-stages.

IV.A.2. Model of Treatment Effects

a) A. Background of TPO

The major sites of TPO production are the liver and kidney. TPO is alsoproduced in the spleen and bone marrow, but the production rate in theseorgans is 5 times lower than in the liver and kidney For backgrounddetails, see, Alexander W S: Thrombopoietin. Growth Factors. 1999;17(1); pp. 13-24; Sungaran R, Markovic B, Chong B H: Localization andregulation of Thrombopoietin mRNA expression in human kidney, liver,bone marrow, and spleen using in situ hybridization. Blood. January1997; Vol. 89(1); pp. 101-107; Nagata Y, Shozaki Y, Nagahisa H, NagasawaT, Abe T, Todokoro K: Serum Thrombopoietin level is not regulated bytranscription but by the total counts of both megakaryocytes andplatelets during Thrombocytopenia and Thrombocytosis. Thromb Haemost.1997; Vol. 77; pp. 808-814; Nagahisa H, Nagata Y, Ohnuki T, Osada M,Nagasawa T, Abe T, Todokoro K: Bone marrow stromal cells produceThrombopoietin and stimulate megakaryocyte growth and maturation butsuppress proplatelet formation. Blood. February 1996; Vol. 87(4); pp.1309-1316; and Rasko J E J, Begley C G: Molecules in focus: TheThrombopoietic factor, Mpl-ligand. Int J Bioch Cell Biol. 1998; Vol. 30:657-660.

Some low TPO production has also been found in many other sites in thebody. For background details, see Nagata Y, Shozaki Y, Nagahisa H,Nagasawa T, Abe T, Todokoro K: Serum Thrombopoietin level is notregulated by transcription but by the total counts of bothmegakaryocytes and platelets during Thrombocytopenia and Thrombocytosis.Thromb Haemost. 1997; Vol. 77; pp. 808-814; and Wichmann H E, GerhardtsM D, Spechtmeyer H, Gross R: A mathematical model of Thrombopoiesis inrats. Cell Tissue Kinet. 1979; Vol. 12; pp. 551-567.

Rates of liver and kidney TPO production are constant underThrombocytopenia and Thrombocytosis of varying degrees of severity. Forbackground details, see, Alexander W S: Thrombopoietin. Growth Factors.1999; 17(1); pp. 13-24; Sungaran R, Markovic B, Chong B H: Localizationand regulation of Thrombopoietin mRNA expression in human kidney, liver,bone marrow, and spleen using in situ hybridization. Blood. January1997; Vol. 89(1); pp. 101-107; and Nagahisa H, Nagata Y, Ohnuki T, OsadaM, Nagasawa T, Abe T, Todokoro K: Bone marrow stromal cells produceThrombopoietin and stimulate megakaryocyte growth and maturation butsuppress proplatelet formation. Blood. February 1996; Vol. 87(4); pp.1309-1316.

TPO production in the spleen and bone marrow is inversely related to themegakaryocyte mass, but the actual contribution is negligible withregard to total TPO production. For background details, see, Alexander WS: Thrombopoietin. Growth Factors. 1999; 17(1); pp. 13-24; and SungaranR, Markovic B, Chong B H: Localization and regulation of ThrombopoietinmRNA expression in human kidney, liver, bone marrow, and spleen using insitu hybridization. Blood. January 1997; Vol. 89(1); pp. 101-107.

Another mechanism of TPO concentration regulation is receptor-mediatedTPO uptake, since TPO-receptors on the platelet and megakaryocytesurfaces are the main TPO-clearance mechanism. Thus, TPO concentrationis inversely related to the total platelet and megakaryocyte mass. Forbackground details, see, Alexander W S: Thrombopoietin. Growth Factors.1999; 17(1); pp. 13-24; Harker L A: Physiology and clinical applicationsof platelet growth factors. Current Opinion Haematol. 1999; Vol. 6; pp.127-134; Hsu H C, Tsai W H, Jiang M L, Ho C H, Hsu M L, Ho C K, Wang SY: Circulating levels of Thrombopoietic and inflammatory cytokines inpatients with clonal and reactive Thrombocytosis. J Lab Clin Med. 1999;Vol. 134(4); pp. 392-397; Stoffel R, Wiestner A, Skoda R C:Thrombopoietin in Thrombocytopenic mice: evidence against regulation atthe mRNA level and for a direct regulation role of platelets. Blood.January 1996; Vol. 87(2); pp. 567-573; Alexander W S: Thrombopoietin andthe c-Mpl receptor: insights from gene targeting. Int J Biochem CellBiol. 1999 October; Vol. 31(10); pp. 1027-1035. [ABSTRACT]; Miyazaki M,Fujiwara Y, Isobe T, Yamakido M, Kato T, Miyazaki H: The relationshipbetween carboplatin AUC and serum Thrombopoietin kinetics in patientswith lung cancer. Anticancer Research. 1999; Vol. 19; pp. 667-670; andRasko J E J, Begley C G: Molecules in focus: The Thrombopoietic factor,Mpl-ligand. Int J Bioch Cell Biol. 1998; Vol. 30: 657-660.

The effects of TPO on the Thrombopoietic line may be divided into threetypes: (i) stimulation of proliferation of megakaryocyte progenitorsthat have an ability to proliferate; (ii) stimulation of maturation ofall megakaryocyte progenitors; (iii) induction of additional endomitosisof already mature megakaryocytes, which leads to an increase in themodal megakaryocyte ploidy. For background details, see, Kaushansky K:Thrombopoietin: the primary regulator of platelet production. Blood.July 1995; Vol. 86(2), pp. 419-431; Somlo G, Sniecinski I, ter Veer A,Longmate J, Knutson G, Vuk-Pavlovic S, Bhatia R, Chow W, Leong L, MorganR, Margolin K, Raschko J, Shibata S, Tetef M, Yen Y, Forman S, Jones D,Ashby M, Fyfe G, Hellmann S, Doroshow J H: Recombinant HumanThrombopoietin in combination with Granulocyte colony-stimulating factorenhances mobilization of peripheral blood progenitor cells, increasesperipheral blood platelet concentration, and accelerates haematopoieticrecovery following high-dose chemotherapy. Blood. May 1999; Vol. 93(9);pp. 2798-2806; Murray L J, Luens K M, Estrada M F, Bruno E, Hoffman R,Cohen R L, Ashby M A, Vadhan-Raj S: Thrombopoietin mobilizes CD34⁺ cellsubsets into peripheral blood and expand multilineage progenitors inbone marrow of cancer patients with normal haematopoiesis. Exp Hem.1998; Vol. 26; pp. 207-216; Vadhan-Raj S, Murray U, Bueso-Ramos C, PatelS, Reddy S P, Hoots W K, Johnston T, Papadopolous N E, Hittelman W N,Johnston D A, Yang T A, Paton V E, Cohen R L, Hellmann S D, Benjamin RS, Broxmeyer H E: Stimulation of megakaryocyte and platelet productionby a single dose of recombinant human Thrombopoietin in patients withcancer. Ann Intern Med. May 1997; Vol. 126(9); pp. 673-681; Wichmann HE, Gerhardts M D, Spechtmeyer H, Gross R: A mathematical model ofThrombopoiesis in rats. Cell Tissue Kinet. 1979; Vol. 12; pp. 551-567;Harker L A, Roskos L K, Marzec U M, Carter R A, Cherry J K, Sundell B,Cheung E N, Terry D, Sheridan W: Effects of megakaryocyte growth anddevelopment factor on platelet production, platelet life span, andplatelet function in healthy human volunteers. Blood. 2000 April; Vol.95(8); pp. 2514-2522; Swinburne J L, Mackey M C: CyclicalThrombocytopenia: characterization by spectral analysis and a review. JTheor Medicine. 2000; Vol. 2; pp. 81-91; Rasko J E J, Begley C G:Molecules in focus: The Thrombopoietic factor, Mpl-ligand. Int J BiochCell Biol. 1998; Vol. 30: 657-660; and De Sauvage F J, Carver-Moore K,Luoh S-M, Ryan A, Dowd M, Eaton D L, Moore M W: Physiological regulationof early and late stages of megakaryocytopoiesis by Thrombopoietin. JEsp Med. 1996 February; Vol. 183: 651-656.

b) Mathematical Model of TPO Effects

TPO concentration effects on the Thrombopoiesis line is now considered.As discussed above, three things depend on TPO concentration: (i)amplification rate (amp), (ii) the rate of cell maturation or,alternatively, transit time through a given compartment (transit), and(iii) the fraction of megakaryocytes of given ploidy that undergoadditional endomitosis and pass on to the next ploidy class.

(1) TPO Concentration

Recombinant human full-length TPO and its truncated form rHuMGDF arefully active biologically. Therefore, in our model we add exogenouslyadministered recombinant protein to endogenously produced TPO in orderto calculate actual TPO concentration (c).

As mentioned above, the rate of TPO production in the main TPOproduction sites, i.e. liver and kidney, is constant underThrombocytopenia or Thrombocytosis. For background details, see,Alexander W S: Thrombopoietin. Growth Factors. 1999; 17(1); pp. 13-24;Sungaran R, Markovic B, Chong B H: Localization and regulation ofThrombopoietin mRNA expression in human kidney, liver, bone marrow, andspleen using in situ hybridization. Blood. January 1997; Vol. 89(1); pp.101-107; and Nagata Y, Shozaki Y, Nagahisa H, Nagasawa T, Abe T,Todokoro K: Serum Thrombopoietin level is not regulated by transcriptionbut by the total counts of both megakaryocytes and platelets duringThrombocytopenia and Thrombocytosis. Thromb Haemost. 1997; Vol. 77; pp.808-814.

The level of TPO mRNA in sites like the bone marrow and spleen, where itis produced in a 5-fold lower rate than in the liver and kidney, is notsignificantly different from the TPO level in peripheral blood. Forbackground details, see Hsu H C, Tsai W H, Jiang M L, Ho C H, Hsu M L,Ho C K, Wang S Y: Circulating levels of Thrombopoietic and inflammatorycytokines in patients with clonal and reactive Thrombocytosis. J LabClin Med. 1999; Vol. 134(4); pp. 392-397.

Therefore, the assumption is made that the bone marrow and spleencontributions to the total TPO concentration are insignificant.Endogenously produced TPO is assumed to have a constant rate ofproduction p. However, this number can change.

The main mechanism that controls TPO concentration in the blood isreceptor-mediated TPO uptake (u). For background details, see, AlexanderW S: Thrombopoietin. Growth Factors. 1999; 17(1); pp. 13-24; Harker L A:Physiology and clinical applications of platelet growth factors. CurrentOpinion Haematol. 1999; Vol. 6; pp. 127-134; Hsu H C, Tsai W H, Jiang ML, Ho C H, Hsu M L, Ho C K, Wang S Y: Circulating levels ofThrombopoietic and inflammatory cytokines in patients with clonal andreactive Thrombocytosis. J Lab Clin Med. 1999; Vol. 134(4); pp. 392-397;Stoffel R, Wiestner A, Skoda R C: Thrombopoietin in Thrombocytopenicmice: evidence against regulation at the mRNA level and for a directregulation role of platelets. Blood. January 1996; Vol. 87(2); pp.567-573; Alexander W S: Thrombopoietin and the c-Mpl receptor: insightsfrom gene targeting. Int J Biochem Cell Biol. 1999 October; Vol. 31(10);pp. 1027-1035. [ABSTRACT].

Another mechanism of TPO removal from the blood is non-specificTPO-receptor-independent clearance (I). This mechanism is ratherinsignificant in the normal state, when receptor-mediated TPO binding,endocytosis, and degradation remove most of the TPO. Thus, the formulathat calculates TPO concentration hourly is given in Equation 1 asfollows:C* _(i+1) =C _(i) +p+x _(i) −u _(i) −l _(i) p,x _(i) ,u _(i) ,l _(i)≧0 C_(i)>0  (1)where Ci is TPO concentration at the current hour (i); C*i+1 isapproximation of the TPO concentration at the next hour (detailedbelow); p is TPO concentration produced per hour endogenously; xi is theaddition to TPO concentration due to exogenous TPO administration; ui isTPO concentration removed from the blood by receptor-mediated binding;li is TPO concentration cleared from circulation by non-specificmechanisms.

It is assume that receptor-mediated TPO clearance depends on the totalnumber of TPO receptors (n) and on the ability of each receptor touptake TPO (a):u _(i) =n _(i) ·a n _(i) ,a≧0  (2)where n_(i) represents the receptor pool and a is TPO-clearing abilityof the receptors, i.e. amount of TPO that each receptor removes perhour.Both, megakaryocyte and platelet mass contribute to the total receptornumber (n) and, thus, to the rate of TPO clearance (u). 15 We assumethat every platelet bears the same number of TPO receptors (mPL). Thereceptor number on megakaryocytes, however, changes. Thus, the receptorpool (n) is:

$\begin{matrix}{{n_{i} = {{\sum\limits_{{comp} = 1}^{4}\left( {\sum\limits_{j = 1}^{\lbrack\tau_{comp}\rbrack}\left( {q_{{comp},j,i} \cdot m_{{comp},j}} \right)} \right)} + {q_{PLi} \cdot m_{PL}}}}{q_{{comp},j,i},q_{{PL},i},m_{{comp},j},{m_{PL} \geq 0}}} & (3)\end{matrix}$where comp (1 to 4) is one of the platelet releasing megakaryocytecompartments (MK16, MK32, MK64, MK128, respectively); j is the period(in hours) that a given megakaryocyte already spent in the specificcompartment; [τ] denotes τ rounded to an integer; q_(comp,j,i) is thequantity of the megakaryocytes of the specific compartment (comp), whichspent a given period (j) in it; m_(comp,j), is the receptor number ongiven megakaryocyte; q_(PL) i is the platelet number; m_(PL) is thereceptor number per platelet.

It is assumed that the number of TPO receptors on each megakaryocyte(m_(comp,j)) equals the number of platelets that the megakaryocyte iscapable of releasing (c_(comp)) times the average number of receptorsper every potential platelet (b).m _(comp,j)=(c _(comp) −r _(comp) ·j)·b c _(comp) ,r _(comp) ,j,b≧0  (4)where ccomp is the number of platelets that the megakaryocyte of thespecific compartment comp can release during its entire life-span(τ_(comp)); rcomp is the rate of platelet release by the megakaryocyte;j is the period that this megakaryocyte already spent in thiscompartment; b is the number of receptor on the megakaryocyte perpotential platelet.

It is also assumed that the non-specific TPO clearance (l_(i)) isexponential, i.e. every hour some fraction (f) of a current amount ofTPO (c_(i)) is removed from circulation:l _(i) =f·C _(i) f≧0  (5)where f is the coefficient of non-specific TPO clearance and c_(i) isthe current TPO concentration. Other modes of non-specific TPO removalcan be assumed as well. Exogenous TPO is included in the model as alinear relation of the initial maximum TPO blood concentration (x_(i))to the administered intravenous (IV) dose(s) (the relation coefficientis 0.0167) 21:x _(i)=0.0167·s _(i) s _(i)≧0  (6)The state when TPO completely disappears from the blood seems veryunlikely based on biological logic, so we restricted the lower limit ofpossible TPO concentration to certain minimum ε (positive). Thus, theequation (1) is modified to receive the full TPO concentration equation:C _(i+1)=max((C _(i) +p+x _(i) −a·n _(i) −f·C _(i)),ε) ε>0  (7)In steady state, the TPO concentration (C) is constant.

(2) TPO Effects on Amplification Rate

In the disclosed model, there are only two compartments, SC compartment30 and CFU-Meg compartment 40, whose cells are capable of dividing.These compartments differ significantly from each other, thus, we shalldiscuss them separately. Cells of other model compartments do notproliferate, and so their amplification rate equals 1 under allcircumstances.

SC compartment 30:

Since TPO is primarily a Thrombopoiesis-stimulating cytokine, we assumethat the cells, which are not committed to Thrombopoietic line yet (theSC compartment in our model), are relatively insensitive to TPO,compared to committed megakaryocytic cells. In the disclosed model thisis considered as a threshold (θ) in TPO concentration. Only above thisthreshold (θ) TPO affects stem cells. As long as TPO remains below thethreshold (θ), stem cells in the model are regulated by intrinsicTPO-independent mechanism that keeps the size of their population almostconstant.

Thus, below the threshold (θ), SC amplification rate (α_(SC)) isdetermined hourly depending on the current number of cells in the SCcompartment. It is biologically reasonable that the dependence equationis a sigmoidal function where α_(SC) changes from 1 (i.e., noamplification, the cell number remains the same) when the cell numberapproaches infinity, up to the maximal value α_(SCw) when the cellnumber approaches zero. The increase in amplification rate (α_(SC)) isrelatively gradual as long as the cell number (q_(SCi)) exceeds certaincritical value (we assumed it to be a fraction (v) of the normal cellnumber (q_(SCnorm))). However, when the cell number falls bellow thisthreshold, α_(SC) begins to increase rapidly in order to restore the SCcompartment as soon as possible. It is assumed that at normal cellnumbers (q_(SCnorm)), α_(SCi) should be a fraction (γ) of its maximalvalue α_(SCw). Following is an example of such equation:

$\begin{matrix}{\underset{C_{i} \leq \theta}{\alpha_{{SC},{i + 1}}^{*}\left( {q_{{SC},i},C_{i}} \right)} = \left\{ \begin{matrix}{{{\left( {\alpha_{{SC}\mspace{11mu} w} - 1} \right) \cdot \frac{1}{{\left( {\frac{1}{y} - 1} \right) \cdot \left( \frac{q_{{SC},i}}{q_{{SC}\mspace{14mu}{norm}}} \right)^{S_{1}}} + 1}} + 1},} & {q_{{SC},i} \geq {v \cdot q_{{SC}\mspace{14mu}{norm}}}} \\{{\alpha_{{SC}\mspace{11mu} w} - {\left( {\alpha_{{SC}\mspace{11mu} w} - \alpha_{SC}^{\sim}} \right) \cdot \left( \frac{q_{{SC},i}}{v \cdot q_{{SC}\mspace{11mu}{norm}}} \right)^{S_{2}}}},} & {q_{{SC},i} < {v \cdot q_{{SC}\mspace{11mu}{norm}}}}\end{matrix} \right.} & (8) \\{\mspace{79mu}{\alpha_{SC}^{\sim} = {{\left( {\alpha_{{SC}\mspace{11mu} w} - 1} \right) \cdot \frac{1}{{\left( {\frac{1}{y} - 1} \right) \cdot v^{S_{1}}} + 1}} + {1{\begin{matrix}{q_{SC},S_{1,2},{\theta \geq 0}} \\{\alpha_{{SC}\mspace{11mu} w} \geq 1} \\{{0 < y},{v \leq 1}}\end{matrix}}}}}} & \;\end{matrix}$

where α*_(SC,i+1) is the amplification rate calculated based solely onthe cell number; α_(SCw) is the maximal possible rate of cellamplification in the SC compartment when TPO concentration (Ci) is belowthe threshold; q_(SC,i) is a quantity of cells in the SC compartment;q_(SC) norm is the normal quantity of cells there. S1 and S2 are thesensitivity coefficients in the regions of q_(SC,i) higher or lower thanthe critical value (vq_(SCnorm)), respectively. These values determinethe sensitivity of the mechanism that links the amplification rate(α_(SC)) with the cell number (q_(SC,i)). In other words, they determinethe steepness of the dependence curve in the corresponding regions. HighS1 or S2 mean that α_(SC) changes significantly due to slight changes ofq_(SC), and low S1 or S2 mean that α_(SC) remains relatively constantwhatever the changes of q_(SC) are. Distinguishing between S1 and S2allows us to force the amplification rate (α_(SC)) to grow rapidly asthe cell number (q_(SC,i)) falls below the critical value, therebyincreasing the resistance of the system to further cell number(q_(SC,i)) decay. Although the symbols S1 and S2 appear in severalequations, their values are specific for every equation.

It is suggested that TPO concentration (C) increase above the thresholdshould occur in severe platelet and/or megakaryocyte deficiency, or whenTPO is administered exogenously. It is assumed that at thesecircumstances, TPO further increases the rate of cell amplification inthe “Stem Cell” compartment (α_(SC)). It is also assumed that theincrease is proportional to the difference between actual TPOconcentration (Ci) and the threshold. Thus, TPO effects appear graduallyfrom the zero increase, when TPO concentration (Ci) equals thethreshold. Saturation of the mechanisms of TPO effect is reflected inthe concavity of the effect function.

The following is an example of such a function:

$\begin{matrix}{{{\alpha_{{SC},{i + 1}}\underset{C_{i} > \theta}{\left( {q_{{SC},i},C_{i}} \right)}} = {{\alpha_{{SC},{i + 1}}^{*}\left( {q_{{SC},i},C_{i}} \right)} + {t \cdot {\ln\left( {C_{i} - \theta + 1} \right)}}}}{t,{\theta \geq 0}}} & (9)\end{matrix}$

where α*_(SC,i+1) is the same expression as in equation (8), i.e.amplification calculated based on a TPO-independent mechanism, and thesecond operand is the TPO-related contribution to the amplification rate(α_(SC,i+1)). t determines the steepness of the dependence curve (t isnon-negative). Although the symbol t appears in several equations, itsvalue is specific for every equation. One is added to the In argument inorder to ensure positivity of the In result.

CFU-Meg Compartment 40:

In contrast to the cells of the SC compartment, we assume that cells ofthis compartment are fully sensitive to TPO and respond to the absoluteTPO concentration (Ci), not to its difference with a threshold (Ci−θ).In the disclosed model, there is no TPO-independent proliferativemechanism, and CFU-Meg cease to proliferate when deprived of TPO. On theother hand, when TPO concentration (Ci) in the system increases, α_(CFU)does not rise to infinity, but rather gradually reaches saturation,which also seems reasonable biologically. At normal TPO concentrations(C_(norm)), we assume α_(CFU) to be a fraction (h) of its maximal value(α_(CFUmax)). Thus an equation that describes the relation of theamplification rate of CFU-Meg cells (α_(CFU)) to TPO concentration (Ci)represents a sigmoidal function with α_(CFU) equaling 1 when TPOconcentration (Ci) is zero, passing through h times α_(CFUmax) when TPOconcentration is normal (Ci), and approaching an asymptote in α_(CFUmax)when TPO concentration (Ci) approaches infinity. In addition, in orderto enable the system to be sensitive both to the regulation byendogenously produced TPO and to the effect of the exogenouslyadministered drug, it was assumed that the function changes relativelyrapidly in the region of normal TPO concentration (C_(norm)) and with amuch smaller rate when a TPO concentration (Ci) is somewhat higher thannormal (C_(norm)). The following is an example of such a function:

$\begin{matrix}{{\alpha_{{CFU},{i + 1}}\left( C_{i} \right)} = {{\left( {\alpha_{{CFU}\mspace{11mu}\max} - 1} \right) \cdot \left( {1 - \frac{1}{{\frac{1}{\frac{1}{h} - 1} \cdot \left( \frac{C_{i}}{C_{norm}} \right)^{t}} + 1}} \right)} + {1{\begin{matrix}\begin{matrix}{C_{norm} > 0} \\{t \geq 0}\end{matrix} \\{0 < h \leq 1}\end{matrix}}}}} & (10)\end{matrix}$

where α_(CFU,i+1) is an amplification rate of the CFU compartment;α_(CFUmax) is a maximal value of amplification rate there; C_(norm) isnormal TPO concentration; t is the parameter that determines thesteepness of the dependence curve.

(3) TPO Effects on Transit Time

For the reason noted earlier, it is assumed that all platelet-releasingmegakaryocyte compartments have the same transit time (τ_(MK)). It isalso assumed that neither the relation of megakaryocyte volume (andthus, its platelet releasing capacity c_(comp)) nor of its rate ofplatelet release rcomp to megakaryocyte ploidy, is affected by TPO.Therefore, the transit time (τ_(MK)) through the noted compartments isconstant. Platelets also spend in average a constant time in thecirculation (τ_(PL)), which is not affected by TPO concentration (Ci).

In contrast, the transit times of the SC, CFU-Meg, and MKB compartments(τ_(SC), τ_(CFU), τ_(MKB), respectively) are functions of themicro-environmental conditions. Since cells that are far from maturationare not expected biologically to undergo a sudden shift to maturation,it seems that these functions determine the value the transit timeshould approach, rather than the actual transit time. The actual transittime changes gradually: every hour it changes by 1-2 hours towards thefunction-determined value. Thus, the mean of the value is determined,that transit time approaches rather than the transit time itself whenspeaking about transit time (τ) calculations below.

a. SC Compartment:

It is assumed that regarding transit time (τ_(SC)), the SC compartmentdiffers from others in the same way as regarding amplification rate(α_(SC)). It means that the cells of this compartment respond to TPOonly when its concentration (Ci) rises above a threshold (θ). Thisthreshold is the same as for the amplification rate (α_(SC)). Below thethreshold SC transit time is assumed to be regulated by a TPO-unrelatedmechanism dependent on the current cell number (q_(SCi)) only. Thefunction of this dependence changes the transit time from its minimalvalue (τ_(SCu)) when the cell numbers (q_(SCi)) approach infinity,through the normal value that is greater than the minimal one by factorg, up to the highest value ((τ_(SCmax)) determined solely by biologicalreasons. This means that when the cell number in SC compartment(q_(SCi)) is relatively large, the cells will pass relatively rapidly tothe next compartment, thus reducing the SC one; and they will remainlonger in the SC compartment when their number (q_(SCi)) is low, thusrepopulating it. This manner of regulation seems reasonablebiologically.

It is suggested that similar to the amplification rate (α_(SC)), thetransit time (τ_(SC)) in the range of very low cell numbers (q_(SCi))(lower than a certain fraction (v) of the normal (q_(SCnorm))), is verysensitive to further cell number decrease, and grows rapidly, therebyresisting compartment exhaustion. This fraction (v) is the same as forthe SC amplification rate.

Following is an example of such a function:

$\begin{matrix}{\underset{C_{i} \leq \theta}{\tau_{{SC},{i + 1}}^{*}\left( {q_{{SC},i},C_{i}} \right)} = {\left\{ {{\begin{matrix}{{\tau_{{SC}\; u} \cdot \left( {1 + {\left( {g - 1} \right) \cdot \left( \frac{q_{{SC}\;{norm}}}{q_{{SC},i}} \right)^{S_{1}}}} \right)},} & {q_{{SC},i} \geq {v \cdot q_{{SC}\;{norm}}}} \\{{\tau_{{SC}\;{ma}\; x} - {\left( {\tau_{{SC}\;{ma}\; x} - \tau_{SC}^{\sim}} \right) \cdot \left( \frac{q_{{SC},i}}{v \cdot q_{{SC}\;{norm}}} \right)^{S_{2}}}},} & {q_{{SC},i} < {v \cdot q_{{SC}\;{norm}}}}\end{matrix}\mspace{20mu}\tau_{SC}^{\sim}} = {\tau_{SCu} \cdot \left( {1 + {\left( {g - 1} \right) \cdot \frac{1}{v^{S_{1}}}}} \right)}} \right.\begin{matrix}\begin{matrix}\begin{matrix}{S_{1,2} \geq 0} \\{\tau_{{SC}\; u} > 0}\end{matrix} \\{g \geq 1}\end{matrix} \\{0 < v \leq 1}\end{matrix}}} & (11)\end{matrix}$

where τ*_(SC,i+1) is the transit time calculated based on cell numbers(q_(SC,i)) only, i.e. when TPO concentration (Ci) remains below thethreshold; τ_(SCu) is the minimal possible transit time through SCcompartment in these circumstances; v is the fraction of normal cellnumber (q_(SCnorm)), below which the dependence of the transit time(τ*_(SC,i+1)) on the cell number (q_(SC,i)) changes; S1 and S2 are thesensitivity coefficients in the regions of q_(SC,i) lower and higherthan vqSCnorm, respectively.

If TPO concentration (Ci) in the model rises above the threshold, thetransit time (τ_(SC)) is assumed to shorten in a dose dependent manner.As for the amplification rate (α_(SC)), its decrease is presumed to beproportional to the difference between actual TPO concentration (Ci) andthe threshold. However, a shortening of the transit time down to zero byTPO is biologically illogical, so we assume that the transit time(τ_(SC)) approaches some minimal value as TPO concentration (Ci)increases. In our model this minimum represents a fraction (k) of thetransit time calculated on the basis of cell numbers (τ*_(SC,i+1)) asdescribed earlier (equation (11)).

Following is an example of such an equation:

$\begin{matrix}{{{\tau_{{SC},{i + 1}}\underset{C_{i} > \theta}{\left( {q_{{SC},i},C_{i}} \right)}} = {{\tau_{{SC},{i + 1}}^{*}\left( {q_{{SC},i},C_{i}} \right)} \cdot k \cdot \left( {\frac{1}{{t \cdot \left( \frac{C_{i} - \theta}{C^{*} - \theta} \right)^{t}} + \frac{k}{1 - k}} + 1} \right)}}\mspace{20mu}{0 < k \leq 1}\mspace{20mu}{t \geq 0}} & (12)\end{matrix}$

where τ_(SC,i+1) is the transit time when TPO concentration (Ci) ishigher than the threshold; τ*_(SC,i+1) is the transit time calculated onthe basis of cell numbers as described in equation (11); k is thefraction of τ*_(SC,i+1) that gives the minimum transit time approachesas TPO concentration (Ci) increases; C* determines the point of TPOconcentration (Ci), around which the transit time (τ_(SC)) is the mostsensitive to concentration (C) change; t determines the steepness of thedependence curve (t is non-negative). Multiplication by t enables toregulate the sensitivity to Ci with t<1 in the same manner as when t>1.

b. CFU-Meg and MKB Compartments:

-   -   It is assumed that the transit time parameters of these two        compartments (τ_(CFU), τ_(MKB), respectively) are dependent        solely on TPO and respond to the absolute TPO concentration        (Ci), rather than to its difference with a threshold (Ci−θ). As        TPO level (Ci) drops, the cell passage through these        compartments slows, i.e. transit time (τ_(comp)) increases up to        the values limited solely by biological reasons (τ_(comp,max))        (it is assumed that the cells cannot stay in these compartments        for an infinite period of time). On the other hand, when the TPO        concentration (Ci) in the system increases, τ_(comp) does not        shorten to zero, but rather asymptotically reaches τ_(comp,min),        thus bounding the function from below. This also seems        biologically reasonable, as the cells cannot move through the        compartment in one instant. At normal TPO concentrations        (Cnorm), we set τ_(comp) to equal its normal value        (τ_(comp,norm)). In addition, in order to enable the system to        be sensitive both to the regulation by endogenously produced TPO        and to the effect of the exogenously administered drug, it was        assumed that the function changes relatively rapidly in the        region of TPO concentrations (Ci) lower than normal (C_(norm))        and with a smaller rate when a TPO concentration (Ci) is higher        than normal (C_(norm)). The following is an example of such a        function:

$\begin{matrix}{\tau_{{comp},{i + 1}} = {\left\{ \begin{matrix}{{\tau_{{comp},{m\;{ax}}} - {\left( {\tau_{{comp},{{ma}\; x}} - \tau_{{comp},{norm}}} \right) \cdot \left( \frac{C_{i}}{C_{norm}} \right)^{t_{1}}}},} & {C_{i} \leq C_{norm}} \\{{{\left( {\tau_{{comp},{norm}} - \tau_{{comp},{m\; i\; n}}} \right) \cdot \frac{2}{\left( \frac{C_{i}}{C_{norm}} \right)^{t_{2}} + 1}} + \tau_{{comp},{m\; i\; n}}},} & {C_{i} > C_{norm}}\end{matrix}\mspace{20mu}  \right.\begin{matrix}{0 < \tau_{{comp},{m\; i\; n}} \leq \tau_{{comp},{norm}} \leq \tau_{{comp},{m\;{ax}}}} \\{{t_{1,2} \geq 0}\mspace{310mu}}\end{matrix}}} & (13)\end{matrix}$

where comp is one of the aforementioned compartments (CFU-Meg or MKB);τ_(comp,i+1) represents the transit times through these compartments;τ_(comp,min), τ_(comp,norm), and τ_(comp,max) are the minimal, normaland maximal transit times when TPO concentration is normal; t1 and t2determine the steepness of the dependence curve in the regions of Cilower and higher than Cnorm, respectively.

(4) TPO Effects on the Fraction of Cells that Flow from One Compartmentto the Next.

The discussed parameter is the proportion of cells that passes to thenext compartment at any given moment (φ). As was noted earlier, it isassumed that the fraction of the SC that commits to the megakaryocyticlineage (φ_(SC)) is constant and TPO-independent. TPO in our model doesnot affect the two subsequent compartments, CFU-Meg and MKB.

In contrast, the fractions of MK16-, MK32-, and MK64-megakaryocytes thatundergo additional endomitoses and flow to the next compartment(φ_(comp)) are assumed to be in the range of 0 to 1 depending on TPOconcentration (Ci). Because there is no compartment with ploidy greaterthan 128N, the megakaryocytes of the MK128 compartment do not flow toany other compartment.

The dependence of MK16, MK32, and MK64 φ parameters on TPO concentrationassumed to be delayed with φ calculated based on TPO concentration priorto last endomitosis (C_(i−μ)).

In the model, this dependence is expressed by a sigmoidal function withφ set to 0 when TPO concentration (Ci) is 0, equaling the normal value(φ_(norm)) when TPO concentration is normal (C_(norm)), and approaching1 asymptotically.

$\begin{matrix}{{{\varphi_{{comp},{i + 1}}\left( C_{i - \mu} \right)} = {1 - \frac{C_{norm}^{t} \cdot \left( {\frac{1}{\varphi_{{comp},{norm}}} - 1} \right)}{C_{i - \mu}^{t} + {C_{norm}^{t} \cdot \left( {\frac{1}{\varphi_{{comp},{norm}}} - 1} \right)}}}}{0 \leq \varphi_{{comp},{norm}} \leq 1}{t,{\mu \geq 0}}} & (14)\end{matrix}$

where comp is one of the discussed compartments (MK16, MK32, or MK64);φ_(comp,i+1) is a φ parameter of these compartments; μ is the timeneeded for one additional endomitosis; φ_(comp,norm) is the value ofφ_(comp) under normal TPO concentration (C_(norm)); t determines thesteepness of the dependence function (t is non-negative).

The time needed for an additional endomitosis (μ) assumed to be the samein the three relevant compartments (MK16, MK32, and MK64).

IV.A.3. Complete Detailed Model

The complete model was built as an imitation of what happens in realbone marrow. Each compartment is subdivided into small sections thatcontain the cells of a specific age with a resolution of one hour. Forexample, the fifth age-section of MKB compartment 50 contains cellswithin MKB compartment 50 that have been within that compartment for 5hours. Every hour, all the cells in the “bone marrow” pass to the nextage-section in the same compartment.

When the cell has spent all the transit time predetermined for it in agiven compartment, it passes to the next compartment to the zeroage-section. Thus, every hour the cells that leave one compartment fillthe zero age-section of the next one. The cells that leave MK128compartment 90 die. The zero age-section of compartment 30 is filled bya certain fraction of the cells that leave SC compartment 30.

The cells that release platelets add a certain platelet number to thezero age-section of PL compartment 100 every hour. Reference is now madeto FIG. 4, which is an illustration of the implementation of the model.The model is implemented as a chart of 8 rows and 360 columns. The 8rows relate to 8 cell compartments, and the columns relate to the agesections, with the assumption that transit time does not exceed 360hours. This chart is updated hourly according to the rules describedabove.

Reference is now made to FIG. 5, which shows a graphical representationof the chart of FIG. 4. Within the compartments where proliferationoccurs (SC and CFU-Meg), the number of proliferating cells increasesfrom the first to the last age-section. In contrast, the cell number inthe compartments that have no proliferating ability remains constant(MKB, MK128, PL), or decreases when cells that have undergone additionalendomitosis leave the compartment for the next one (MK16, MK32, MK64).

Reference is now made to FIG. 6, which is an illustration of anotherrepresentation of the model, based on the time courses of differentcompartments. The rows in the chart represent cell compartments and thecolumns represent time of simulation course. At every time-step of thesimulation (one hour of “patient's life”), the number of cells in allage-sections is summarized for each compartment and the next column intime-course chart (FIG. 6) is filled. Thus, every cell in the chartrepresents the total number of cells in a given compartment at a giventime point.

There is an additional row in the time-course chart that relates to theTPO concentration in the blood. TPO concentration is monitored andout-put every time-step concurrently with the cell numbers.

Reference is now made to FIG. 7, which is a graphical representation ofthe chart of FIG. 6, and is the most useful model output Theimplementation of the described model results in a computer simulatorthat describes the changes that occur in the human Thrombopoietic system(platelet counts, bone marrow precursor numbers, and TPO concentration)over a time span that may last several years. The resolution of thesimulator output is one hour.

Time units and periods that will mentioned hereafter relate to thesimulated patient's life, rather to the running time of the program.

IV.A.4. Parameter-Specific Adaptation of Model

This model may be fit to patients with diverse blood and bone marrowparameters. People differ in their baseline platelet counts and numbersof bone marrow precursors, in the sensitivity of their stem cell“intrinsic” regulation mechanism, in their minimum and normal transittimes and maximal amplification rates, rates of platelet release bymegakaryocytes, fractions that each megakaryocyte ploidy classcontribute for additional endocytosis, and the time needed forendomitosis (μ). Furthermore, the baseline TPO level, the rate of TPOproduction, receptor- and non-receptor-mediated TPO clearance, thethreshold of TPO effect on the SC compartment, and the sensitivity ofdifferent cell parameters to TPO also differ between patients.

To obtain an ideal fitness of the model to each patient, thepatient-related parameters should be given individually for eachpatient. However, practically, it would be extremely difficult topredetermine many of these parameters for every patient. Therefore,certain average parameters have been calculated based on published data,and are shown in Table 1 below. These averaged parameters are used as aframework into which known individual characteristics are included.Thus, before a particular simulation is begun, relevant knowninformation about the individual may be included, sometimes replacingcertain parameters of the model.

TABLE COMMON PARAMETERS Compartment Parameter SC CFU-Meg MKB MK16 MK32MK64 MK128 PL q_(norm) 480 650 5959 3900 1380 15 3 17,857,000 (×1000/kgbody weight) τ_(min) 12 30 143 — — — — — (τ_(u) in SC) (hours) τ_(norm)— 60 186 250 250 250 250 240 (hours) τ_(max) 350 360 360 — — — — —(hours) φ_(norm) 0.2846 1 1 0.2682 0.0128 0.1685 — — (/hour) c — — —4000 8000 16000 32000 — (platelets) r — — — 11.19 22.38 44.76 89.52 —(platelet/hr) STEEPNESSES (t) OF THE TPO-SENSITIVITY CURVES a_(SC)a_(CFU) τ_(SC) τ_(CFU) (t₁) τ_(CFU) (t₂) τ_(MKB) (t₁) τ_(MKB) (t₂)φ_(MK16) φ_(MK32) φ_(MK64) 0.02 0.1 0 10⁻¹⁰ 1 1 1 2 2 4 SC-RELATEDPARAMETERS S₁ for S₂ for S₁ for S₂ for v a_(SC) a_(SC) τ_(SC) τ_(SC) ka_(τv) y g 0.01 0.5 0.5 1 0 0.5 1.116 0.25 5 TPO-RELATED PARAMETERS p θf a (pg/ml/hr/ C_(norm) ε C* (pg/ml) (pg/ml) (/hr) receptor molecule)(pg/ml) (pg/ml) (pg/ml) 48 10,000 0.1 38 100 0.01 θ + 50 OTHERPARAMETERS d μ (fraction from each (hours) m_(PL) b a_(CFUmax) hage-section per hour) 16 220 220 1.204 0.125 2.59 × 10⁻⁴

Usually, the known patient-related data are not parameters in the formdefined by our model, but rather measurements obtained in the clinic(e.g., day and value of post-chemotherapy Thrombocytopenia nadir, dayand value of platelet peak after TPO administration, change inmegakaryocyte modal ploidy following some perturbation, etc.). In thesecases, the available data is converted into a model-compatible format.

Sometimes, the only available patient-related data are the graphicrepresentation of the patient's platelet course following someperturbation (e.g., cell-suppressive therapy or TPO administration). Thedata may also be a picture of the platelet course without any externaldisturbance (e.g., cyclic Thrombocytopenia). In these cases the modelparameters are changed by trial-and-error until a good compliance of themodel graphic output and the patient's graphs is achieved. It should benoted, however, that even in the case of trial and error, the choices ofparameter sets are not random but rather are also based on someanalysis.

Specifically, the following tools are available for providing maximumflexibility:

-   -   1) The user can set the baseline values and all other known        patient-specific Thrombopoietic parameters before starting the        simulation.    -   2) The user (e.g., physician) can determine how long of a time        period to simulate, from a number of hours up to several years.    -   3) The user can determine the frequency of showing the course of        a patient counts up to the moment. The frequency can change from        as much as every 12 hours to once during the overall period of        simulation.    -   4) The user can determine the resolution of the output graph,        from the hourly representation of the patient's state down to        any other resolution.    -   5) The user can choose to view the graphical representation of        the age distribution through the compartments at any moment of        the simulation.    -   6) The user can simulate a cell-suppressive therapy at any        moment while running the simulation by reducing one or several        of the compartments by any value.    -   7) The user can simulate exogenous TPO administration at any        moment while running the simulation by controlling dose height,        number of dosings or frequency of dosings.

The simulation tool has been carefully tested with respect to thepublished experimental results, and has proved to be well calibrated foraverage human data. Parameters may be modified relatively quickly forefficient use of the system. The following model parameters areimportant for individualized adjustment of the model:

-   -   baseline number of: SC, CFU-Meg, MKB, MK16, MK32, platelets.    -   amplification rate of: SC, CFU-Meg.    -   transit time of: MKB, MK16, MK32, MK64.    -   fraction undergoing additional endomitosis in: MK16, MK32, MK64.    -   rate of platelet release of: MK16, MK32, MK64, MK128.    -   Time needed for additional endomitosis.    -   Rate of endogenous TPO production.    -   Ratio of receptor- and non-receptor-mediated TPO clearance.    -   Steepness of the sensitivity curve of: CFU-Meg amplification        rate; MKB transit time; MK16, MK32, and MK64 fraction undergoing        additional endomitosis.        Reference is now made to FIGS. 8A, 8B, 9A and 9B, which show a        comparison between experimentally obtained data and the        simulated model. Experimentally obtained in vivo platelet counts        following TPO administration are shown in FIG. 8A and        chemotherapy without TPO is shown in FIG. 9A. FIGS. 8B and 9B        show simulations of the same. By using a TPO schedule designed        by the described model, one can obtain platelet profiles that        are similar to those obtained clinically (FIG. 8B) or even more        effective (FIG. 9B). In this case, these results are achieved by        administering a pre-calculated TPO protocol whose total dose        amounts to 25% of the original total dose.

The complete model simulates cell and platelet counts in the steadystate, as well as after perturbations to the haematopoietic system,e.g., cell-suppressive therapy, recombinant Thrombopoietinadministration for uses such as platelets harvesting, etc. It ispossible to simulate any protocol of drug administration and anyhaematological state of a patient, regarding his/her platelet count andnumber of bone marrow megakaryocytes and their precursors. The model canbe adapted to many categories of patients, or healthy platelet donors.It can also be modified to fit species other than human. By providingspecific parameters one can adjust the model so as to yield particularpredictions about the Thrombopoietic profile of an individual patient.Other platelet disorders, such as cyclic Thrombocytopenia, may also besimulated.

IV.B. Neutrophil Production in the Bone Marrow and its Concentration inthe Peripheral Blood Compartment Alone or Under the Effects ofGrowth-Factors and Treatment with Granulocyte Colony Stimulating Factor(G-CSF)

Another embodiment of the present invention involves the disclosedtechniques for Neutrophil lineage, Granulopoietic disorders, includingNeutropenia and its treatment with GCS-F. The Neutrophil lineageoriginates in pluripotent stem cells that proliferate and becomecommitted to the Neutrophil lineage. These cells then undergo gradualmaturation accompanied with further proliferation. The present modeluses the state-of-the-art discrete compartmentalization of thiscontinuous maturation-proliferation process, but is not restricted to itand can easily accommodate other modes of describing this continuousprocess using.

It is customary to divide the neutrophil maturation process in the boneto marrow into three morphologically distinguishable mitoticcompartments: Myeloblasts, promyelocytes and myelocytes.

The myelocytes then mature and lose their capacity to proliferate, andthus enter the post mitotic compartment. In the post-mitotic compartmentthe cells continue their gradual maturation, which is not accompaniedwith proliferation through the three morphologically distinguishablesub-compartments: Metamyelocyte, band and segmented-Neutrophils. Cellsexit the various sub-compartments in the post-mitotic compartment andenter the blood as Neutrophils. They then migrate from the blood to thetissues.

The Granulocyte-Colony Stimulating Factor (G-CSF) generates an increasein blood Neutrophil levels primarily by increasing production in themitotic compartment and shortening the transit time of the post-mitoticcompartment.

Thus, the first compartment of the mitotic pool (myeloblast) receives aninflow of cells from stem-cell precursors. Inflow for each of the othercompartments is from outflow of the previous one, subject tomultiplication factors due to cell replication in the mitotic stages.

Models regarding Granulopoiesis in normal humans and in humans withpathologies of the bone marrow were suggested previously in order togive a coherent description of the kinetics of Granulocytes fromexperimental data. For background details, see, Cartwright G E, Athens JW, Wintrobe M M. 1964. The kinetics of Granulopoiesis in normal man.Blood. 24(6): 780-803;

In recent years Schmitz et al. developed a kinetic simulation model forthe effects of G-CSF on Granulopoiesis (for further details, seeSchmitz, S., Franke, H., Brusis, J., Wichmann, H. E. 1993.Quantification of the Cell Kinetic Effects of G-CSF Using a Model ofHuman Granulopoiesis. Experimental Haematology. 21:755-760), and used itfor the analysis of administration of G-CSF to patients suffering fromcyclic Neutropenia (for further details, see Schmitz, S., Franke, H.,Wichmann, H. E., Diehl, V. 1995. The Effect of Continuous G-CSFApplication in Human Cyclic Neutropenia: A Model Analysis. BritishJournal of Haematology. 90:41-47). However, the data Schmitz rests uponfor his model has been more accurately assessed in recent years by Priceet al. and Chatta et al. For further details, see Price T H, Chatta G S,Dale D C. 1996. Effect of Recombinant Granulocyte Colony-StimulatingFactor on Neutrophil Kinetics in Normal Young and Elderly Humans. Blood.88(1): 335-40; and Chatta G S, Price T H, Allen R C, Dale D C. 1994.Effects of in vivo Recombinant Methionyl Human GranulocyteColony-Stimulating Factor on the Neutrophil Response and PeripheralBlood Colony-Forming Cells in Healthy Young and Elderly AdultVolunteers. Blood. 84(9): 2923-9. Actual empirical data regardingcompartment sizes and their transit times was not incorporated intotheir model despite the importance of these data (For further details,see Dancey J T, Deubelbeiss K A, Harker L A, Finch C A. 1976. NeutrophilKinetics in Man. J Clin Invest. 58(3): 705-15).

IV.B.1. Model of Neutrophil Lineage and Effects of G-CSF

a) G-CSF

The effects of G-CSF on the Neutrophil lineage are relayed in the modelin three stages. The first is the administered amount of cytokine givenat time t, which is marked: G_(adm) ^(t)

The G_(adm) vector serves as the control variable for optimization ofG-CSF administration.

The second stage represents the pharmacokinetic behavior of G-CSF incirculation. It incorporates, for instance, the half-life of G-CSF, andcould in the future be modified to express more of the effects of timeon G-CSF activity. This level is marked: G_(blood) ^(t)

G-CSF is eliminated from the blood in a Poissonic manner according tothe following equation, as stated by Stute N, Furman W L, Schell M andEvans W E in “Pharmocokinetics of recombinant humanGranulocyte-macrophage colony stimulating factor in children afterintravenous and subcutaneous administration” Journal of PharmaceuticalScience, 84(7): 824-828, 1995:

$\begin{matrix}{G_{blood}^{t + 1} = {{G_{blood}^{t}\left( {1 - \frac{\ln\; 2}{{\overset{\sim}{t}}_{1/2}}} \right)} + G_{adm}^{t + 1}}} & (14)\end{matrix}$where {tilde over (t)}_(1/2) is the half-life of G-CSF in the blood, andG_(blood) ¹=G_(adm) ¹.

Recent data by Terashi K, Oka M, Ohdo S, Furudubo T, Ideda C, Fukuda M,Soda H, Higuchi S and Kohno S, in “Close association between clearanceof recombinant human Granulocyte colony stimulating factor (G-CSF) andG-CSF receptor on Neutrophils in cancer patients”, Antimicrobial Agentsand Chemotherapy, 43(1): 21-24, 1999, points to the dependence of thehalf-life of G-CSF on Neutrophil counts. In the absence of exactkinetics of G-CSF effects on the Neutrophil lineage, the half-life isconsidered as a constant, though this could be modified should moreexact information emerge.

Only exogenously produced G-CSF is considered to affect the kineticparameters, and endogenously produced G-CSF levels and effects are setto zero. If more empirical data regarding the production of endogenousG-CSF is made available, it could be incorporated into the equation aswell.

The third and final stage models the pharmacodynamic effects of G-CSF onthe kinetic parameters. As will be elaborated subsequently, thedependence of the various kinetic parameters of the Neutrophil lineageon the level of G-CSF in the blood is assumed to be through eithernon-decreasing concave or non-increasing convex functions. Thisreproduces the effects of saturation that are seen in clinical studieson the effects of G-CSF, such as the study by Duhrsen U, Villeval J L,Boyd J Kannourakis G, Morstyn G and Metcalf D in “Effects of recombinanthuman Granulocyte colony-stimulating factor on haematopoietic progenitorcells in cancer patients”, Blood, 72(6): 2074-2081, 1988. That is,addition of G-CSF carries a lesser effect when its level in circulationis already high.

b) Biological Mode

(1) Mitotic Compartment

Long-term effects of G-CSF administration take place in the mitoticcompartment. Although the major contributor to heightened bloodNeutrophil counts in the short term is the post mitotic compartment'sshortening of transit time due to G-CSF administration, this high levelcannot be maintained over the long term without increased production inthe mitotic compartment.

The mitotic compartment is divided into subcompartments. The kthsubcompartment contains all cells of chronological age between k−1 and khours, relative to the time of entry into the mitotic compartment. Thenumber of cells in subcompartment k at time t is marked as m_(k) ^(t).kε{1 . . . τ}m ₁ ^(t) =l ₁ ^(t)(G _(blood) ^(t))  (15)where τ is the transit time of the entire mitotic compartment, and isassumed to be the same and constant for all cells entering the mitoticcompartment, and l₁ is a vector reflecting the flow of newly committedcells into the mitotic compartment. The biological grounds for thisdefinition is the existence of a myeloid stem cell reservoir, which isknown to supply new committed cells to the mitotic compartment. However,the reservoir's actual kinetics are not very well explored empirically.Therefore l₁ is fixed to levels such that the overall size of themitotic compartment as well as the kinetics of the Neutrophils incirculation would match those obtained empirically.

Any new biological data that emerges may help define the kinetics moreaccurately within the framework of this model, although results of thismodel indicate that the assumption of a constant rate of stem cellsflowing into the mitotic compartment in the absence of G-CSF isplausible. For every nε{1 . . . τ} and for every t, amplification occursat the exit from m_(n) ^(t), according to Equation 15 as follows:m _(n+1) ^(t+1) =m _(n) ^(t)·α_(n)(G _(blood) ^(t))  (16)where:α_(n) is a non-decreasing concave function of G-CSF levels in the blood,which determines the factor of amplification in the hourlysubcompartment n. If, for instance, no amplification occurs atsubcompartment n₀ at time t thenα_(n) ₀ =1∀n,G _(blood) ^(t)1≦α_(n)(G _(blood) ^(t))≦2(17) The size of the morphological sub-compartments in the mitoticcompartment at time t is determined as: (18)

$\sum\limits_{n = n_{0}}^{n_{1}}m_{n}^{t}$Where n₀ is the first hourly sub-compartment of a morphologicalsub-compartment and n₁ is its last hourly sub-compartment. The divisioninto the morphological sub-compartments is used only for fine-tuning ofthe kinetic parameters with the use of experimental data.

The mitotic compartment was modeled with an intention to facilitate thespecific cell-cycle cytotoxic effects of chemotherapy. Therefore,cohorts of one hour are modeled as undergoing a process of maturationand amplification culminating in their entry into the post-mitotic asdescribed below. Effects of chemotherapy may be incorporated into themodel by mapping the various cell-cycle phases (G1, S, G2, M) to thehourly cohorts modeled and formulating a function of the cytotoxiceffects of chemotherapy on these phases.

The experimental literature shows wide agreement regarding the steadystate normal amounts of circulating Neutrohpils, size of thepost-mitotic compartment and the three morphologically distinctsub-compartments of the mitotic compartment, and post-mitotic transittime and amplification rates in the mitotic sub-compartments (see, forexample, Dancey J T, Deubelbeiss K A, Harker L A and Finch C A, in“Neutrophil kinetics” in Man. Journal of Clinical Investigation, 58(3):705-715, 1976; Price T H, Chatta G S and Dale D C, “Effect ofrecombinant Granulocytee colony-stimulating factor on Neutrophilkinetics in normal young and elderly humans”, Blood 88(1): 335-340,1996; and Dresch Mary in “Growth fraction of myelocytes in normal humanGranulopoiesis”, Cell Tissue Kinetics 19: 11-22, 1986). To determineother relevant kinetic parameters, which were either not available inthe literature or were given a wide range by experimentalists, steadystate kinetics was assumed and an iterative process was employed. Theseparameters include the inflow of stem cells to the myeloblastcompartment and the transit times of the mitotic sub-compartments.

The half life of blood Neutrophils and the steady state number ofNeutrophils were taken as 7.6 h and 0.4×10⁹ cells/kg body weight,respectively (taken from Dancey J T, Deubelbeiss K A, Harker L A, FinchC A. 1976. Neutrophil Kinetics in Man. J Clin Invest. 58(3): 705-15).Similarly, the same calculation may be made for each patient that is tobe modeled. This would allow the dynamics of every patient to bedescribed by the simulation. The average size of the post-mitoticcompartment (5.84×10⁹ cells/kg body weight—Dancey J T, Deubelbeiss K A,Harker L A, Finch C A. 1976. Neutrophil Kinetics in Man. J Clin Invest58(3): 705-15) and the transit time of the compartment (160 h—Dancey JT, Deubelbeiss K A, Harker L A, Finch C A. 1976. Neutrophil Kinetics inMan. J Clin Invest. 58(3): 705-15; Dresch, Mary. 1986. Growth Fractionof Myelocytes in Normal Human Granulopoiesis. Cell Tissue Kin. 19:11-22; Price T H, Chatta G S, Dale D C. 1996. Effect of RecombinantGranulocyte Colony-Stimulating Factor on Neutrophil Kinetics in NormalYoung and Elderly Humans. Blood. 88(1): 335-40) are compatible with thesize and half-life of the circulating Neutrophil compartment reported byDancey, thus supporting the steady state analysis.

In order to determine the amount of cells in the hourly sub-compartmentsin the mitotic compartment, all compartments in the lineage were modeledusing a steady state assumption. The number of cells exiting thecirculating Neutrophil pool equals the number of cells exiting the postmitotic compartment, which in turn equals the hourly production of cellsin the mitotic compartment. Thus, the number of cells in the last hourlycohort of the mitotic compartment can be determined from the Neutrophildecay rate, which is available in the literature. However, thiscalculation is based on assumptions that there is no apoptosis in thepost-mitotic compartment. Direct experimental data by Thiele J, Zirbes TK, Lorenzen J, Kvasnicka H M, Scholz S, Erdmann A, Flucke U, Diehl V andFischer R, in “Haematopoietic turnover index in reactive and neoplasticbone marrow lesions: Quantification by apoptosis and PCNA labeling,”Annals of Haematology 75(1-2): 33-39, 1997, suggests that apoptosis isnot a significant phenomenon in normal human bone marrow. The sizecalculated for the mitotic compartment is close to that experimentallyobtained by Dancey and Price, thus supporting the notion that apoptosisis not a significant kinetic factor in the lineage. Values for theproduction of cells in the mitotic compartment can later be modified inlight of new evidence.

Regarding the transit time of the mitotic compartment there is littleagreement in the literature, with a range of 90-160 hours given by mostexperimentalists (see Dresch Mary in “Growth fraction of myelocytes innormal human Granulopoiesis,” Cell Tissue Kinetics 19: 11-22, 1986). Inorder to determine the transit times of the mitotic morphologicalsub-compartments, as in Equation 18, the following constraints wereconsidered:

-   -   1. The sizes of the theoretically obtained morphological        sub-compartments must fit those reported experimentally in        normal human haematopoiesis (Dancey J T, Deubelbeiss K A, Harker        L A, Finch C A. 1976. Neutrophil Kinetics in Man. J Clin Invest.        58(3): 705-15) and under the effects of G-CSF (Price T H, Chatta        G S, Dale D C. 1996. Effect of Recombinant Granulocyte        Colony-Stimulating Factor on Neutrophil Kinetics in Normal Young        and Elderly Humans. Blood. 88(1): 335-40);    -   2. At least 24 hours, the typical cell cycle, must separate        amplification points;    -   3. The size of the last hourly sub-compartment must equal the        hourly production of the mitotic compartment (calculated with        the aforementioned iterative process assuming steady state        kinetics);    -   4. Amplification inside the compartment is set at the levels        determined by Mary, J. Y. 1984. Normal Human Granulopoiesis        Revisited I. Blood data, II. Bone Marrow Data. Biomedicine &        Pharmacotherapy. 38: 33-43, 66-67; and    -   5. The total transit time of the mitotic compartment must be        within the 90-160 hour range.        By using the values shown in Table x, an excellent fit was        obtained within the above-mentioned constraints.

It should be noted that when other alternatives with shorter transittimes were attempted, results could not be obtained that agreed with theliterature regarding the size of the mitotic pool or its production.Furthermore, a fit between our simulation model's results regardingPolymorphonuclear (PMN) cell counts in peripheral blood with empiricaldata could not be achieved without speculating extensively on the natureof G-CSF effects on non-committed stem cells. It should be noted, thatlittle empirical quantitative data is available regarding stem cells.

The effects of G-CSF on this compartment are modeled as an increase inthe rate of cells entering the myeloblasts from the uncommitted stemcell pool, increases in the rates of mitosis, and introduction of newpoints of amplification as shown in Equation 15, 16. Since little datais available regarding the increases in amplification due to G-CSF, aninitial assumption was made that amplification reaches full potential atpoints that under normal conditions undergo an amplification of below afactor of 2. Additionally, it was assumed that the transit time in allmitotic sub-compartments and the typical cell cycle duration are notaffected by G-CSF, based on lack of evidence to the contrary.

Reference is now made to FIGS. 14 and 25 which show a comparison ofNeutrophil production according to the described model and experimentaldata in the literature. Increased Neutrophil production is in accordancewith the Neutrophil counts reported by Price et al. In addition, theseincreases are in accordance with Price's data about Neutrophil bonemarrow pool sizes.

Reproduction of the effect of G-CSF on Neutrophil counts and the mitoticcompartment sizes beyond day 5 of administration was accomplished byassuming an increase (15% with the highest dose of G-CSF) in the rate ofcells entering the myeloblast compartment. Alternatively, G-CSF maychange the behavior of the myeloblast compartment such that some of thecells there undergo self-renewal instead of moving on to thepromyelocyte compartment. However, no empirical data to support this isavailable. The model can be modified in light of new experimental datain the future.

(2) Post-Mitotic Compartment

The different post mitotic compartments seem indistinguishable ininsensitivity to cytotoxic chemotherapy. Therefore, it is biologicallyacceptable and computationally sensible to model this compartment as asingle pool of cells, such that the last hourly cohort of the mitoticcompartment enters the compartment, and a proportion of the cells withinthe compartment enter the Neutrophil pool every hour.

The post mitotic compartment at time t is a single quantity of cellsp^(t), such that:p ^(t+1) =l ₃(G _(blood) ^(t))·p ^(t) +m _(τ) ^(t)  (19)where l₃ is a convex, non-increasing function of G-CSF levels in theblood, which takes values in the range of [0-1]. This definition entailsp^(t)>0.We shall mark as of the outflow from the post mitotic compartment:o ^(t) =m _(τ) ^(i) +p ^(t) −p ^(t+1)  (20)The number of Neutrophils in the circulating blood compartment at time tis marked nt and is modeled as a single quantity of cells, such that:

$\begin{matrix}{n^{t + 1} = {o^{t} + {n^{t}\left( {1 - \frac{\ln\; 2}{t_{1/2}}} \right)}}} & (21)\end{matrix}$where t½ is the half-life of Neutrophils in the blood, as defined in thebiological literature. t½ is assumed to be held constant regardless ofG-CSF levels (Lord B. I, Bronchud, M. H., Owens, S., Chang, J., Howell,A., Souza, L., Dexter, T. M. 1989. The Kinetics of Human GranulopoiesisFollowing Treatment with Granulocyte Colony-Stimulating Factor in vivo.Proc. Natl. Sci. USA. 86: 9499-9503), though this could be easilymodified. The kinetics of Neutrophils in the tissues are not modeled inthis work.This model will be incorporated into an optimization scheme that willhave as its objective function both the aims of minimizing G-CSFadministration and returning the Neutrophil lineage to its normallevels.At G_(blood) ^(t)=0, p^(t)=Π,m_(τ) ^(t) at the normal healthy level wehave the following obvious relationship:

$\begin{matrix}{\frac{\Pi}{T} = {m_{\tau}^{t} = {o^{t} = {\frac{n^{t}}{t_{1/2}} \times \ln\; 2}}}} & (21)\end{matrix}$Which reflects the stability of the steady state.

G-CSF affects the post-mitotic compartment by shortening its transittime (i.e. decreasing l₃). Price notes that the number of cells in thepost mitotic compartment is not significantly changed followingadministration of G-CSF. This determination is based on counts made onday 5 after G-CSF administration. Thus, it can be safely assumed thatany increased production of the mitotic compartment flowing into thepost mitotic compartment is translated over the long-term to an increasein the flow of cells from the post mitotic compartment to the Neutrophilpool. This increased flow is compensated by increased production in themitotic compartment only at a later stage. Therefore, an upper limit tothe number of cells in the post mitotic compartment was set, which is atthe values given as steady state counts (Π).

In brief, the effects of G-CSF on the Neutrophil lineage are modeledduring the first few days primarily as a decrease in the counts of thepost-mitotic compartment, which is then compensated by an increasedproduction in the mitotic pool. This compensation sustains the increasein Neutrophil counts in peripheral blood.

Reference is now made to FIG. 11, which is a graphical illustration of asimulation of the model. Though no empirical data is available on thispoint, simulations of the model predict that the number of cells in thepost-mitotic compartment decreases substantially during the first twodays of G-CSF administration, and then replenishes, so that on the sixthday the counts return almost to their normal levels. This replenishmentlags behind that of Price et al report by a few hours. A testablehypothesis can thus be formulated, i.e., whether using the same G-CSFprotocol Price et al used, there is indeed a nadir on day 3 of thetreatment.

TABLE 1 Simulated kinetics after 15 days of subcutaneous administrationof 300 μg G-CSF/kg weight. Relative Day 0 Day 15 of G- increase in (noG-CSF) CSF treatment compartment (×10⁹ cells/kg. (×10⁹ cells/kg. sizedue to Compartment Body weight) body weight) G-CSF Myeloblasts 0.1400.153 1.09 Promyelocytes 0.582 0.898 1.54 Myelocytes 1.373 3.564 2.60Mitotic Total = 2.10 4.615 2.20 Circulating 0.4 2.35 5.88 NeutrophilsDay 0 values are the mean values Dancey et al (1976) use.

IV.B.2. Neutrophils and G-CSF in the Circulating Blood

The elimination of Neutrophils from peripheral blood follows a Poissondistribution, and can therefore be described as an exponential function,as shown by Cartwright G E, Athens J W, Wintrobe M M. 1964. The kineticsof Granulopoiesis in normal man. Blood. 24(6): 780-803. Therefore therate of cells leaving this compartment is based on half-lifedeterminations available in the literature. Since no direct cytotoxiceffects of chemotherapy have been described for this compartment it isalso modeled as a single pool of cells.

The kinetics of G-CSF is also modeled as an exponential distributionwith a half-life of 3.5 hours (Eq. 14).

The effects of G-CSF on the kinetics of the Neutrophil lineage appearnot to be a linear function of G-CSF administration levels. Since dataprovided in the literature (Chatta G S, Price T H, Allen R C, Dale D C.1994. Effects of in vivo Recombinant Methionyl Human GranulocyteColony-Stimulating Factor on the Neutrophil Response and PeripheralBlood Colony-Forming Cells in Healthy Young and Elderly AdultVolunteers. Blood. 84(9): 2923-9) only refers to two doses (30 and 300μgram/kg body weight) we can only speculate on the effects of otherlevels of G-CSF. After trial and error analysis, it was found thatassuming that the effects of the 300-μgram dose are the maximal, at the30-μgram its effects are about 30% of the maximum.

Reference is now made to FIGS. 12A and 12B, which are graphicalillustrations of the effects of G-CSF at the two doses. The effects as afunction of G-CSF level are connected piece-wise linearly. This way, theNeutrophil levels observed clinically under both the 300 and the30-μgram protocols are obtained.

IV.C. Linear Implementation of the Model

Another embodiment of the present invention is the implementation of theabove model by incorporating it into an optimization scheme that has asits objective function both the aims of minimizing G-CSF administrationand returning the Neutrophil lineage to its normal levels.

Although the above-outlined model may be implemented in any number ofoptimization methods, the disclosed embodiment using linear programmingwas chosen because of its inherent advantages compared with some othertechniques, i.e. its ability to provide an optimal solution usingpartially analytical methods, and therefore being more computationallytractable (Gill 1991). On the other hand, implementation of this modelin linear programming carries with it the disadvantage that certaincomputations must be approximated linearly since they cannot beperformed directly using linear methods. Thus, we shall compare the‘closeness’ of the solution obtained through linear programming withthat obtained through another, non-linear method of optimization.

The significant parts of the model that must be modified due to thelinear programming implementation are the sections in whichmultiplication of two {(x_(min),y_(min),x_(min)·y_(min)),(x_(min),y_(max),x_(min)·y_(max)), (x_(max),y_(min),x_(max)·y_(min)),(x_(max),y_(max),x_(max)·y_(max))} variables is defined, since thisoperator is not itself linear. Therefore, multiplication is defined asan approximated value constrained within piecewise linear constraintsthat most closely bound the product within a four-faced to polyhedron in3-dimensional space whose vertices are

Where x_(min), x_(max), y_(min), y_(max) are the constant biologicallydefined minima and maxima of x and y.

$\begin{matrix}{{M\left( {x,y} \right)}\left\{ \begin{matrix}{\geq {{y_{m\; i\; n}x} + {x_{m\; i\; n}y} - {x_{m\; i\; n}y_{{m\; i\; n}\;}}}} \\{\geq {{y_{{ma}\; x}x} + {x_{{ma}\; x}y} - {x_{{ma}\; x}y_{{ma}\; x}}}} \\{\leq {{y_{m\; i\; n}x} + {x_{{ma}\; x}y} - {x_{{ma}\; x}y_{m\; i\; n}}}} \\{\leq {{y_{{ma}\; x}x} + {x_{m\; i\; n}y} - {x_{m\; i\; n}y_{{ma}\; x}}}}\end{matrix} \right.} & (22)\end{matrix}$

Multiplication may also be approximated with variations on the linearleast squares method, by finding one plane that's closest to the fourvertices defined.

The other functions that need to be defined linearly are thoseconcerning the pharmacodynamics of G-CSF. Due to the nature of thesefunctions (either non-increasing convex or non-decreasing concave),these effects are implemented as piece-wise linear functions whosebreakpoints are the doses for which actual experimental data isavailable (Chatta G S, Price T H, Allen R C, Dale D C. 1994. Effects ofin vivo Recombinant Methionyl Human Granulocyte Colony-StimulatingFactor on the Neutrophil Response and Peripheral Blood Colony-FormingCells in Healthy Young and Elderly Adult Volunteers. Blood. 84(9):2923-9). Note that the effects of G-CSF on each of the kineticparameters have not been determined in a detailed manner byexperimentalists. Rather its effects over a few dose levels on theNeutrophil blood counts and the size of the morphologically differentmitotic compartments and the post mitotic compartment have beendetermined. From these data, the effects of G-CSF on the actual kineticparameters (probability of mitosis, transit time and inflow of cellsinto the myeloblast compartment from stem cell progenitors) has beenreconstructed at the dose levels available in the literature. Thesepoints are then connected linearly to obtain piecewise linear functionsrelating G-CSF levels to their effect on those parameters. Furtherexperimental data in the future could be used to produce more accuratefunctions.

At the amplification points within the mitotic compartment, the linearlyapproximated multiplication operator (Eq 22) is used instead of theproduct defined in Eq. 16.

At points where no amplification occurs the quantity from onecompartment is simply transferred to the next according to the followingEquation:

$\begin{matrix}{{m_{n + 1}^{t + 1} = m_{n}^{t}}m_{n}^{0}} & (23)\end{matrix}$Values are set according to the steady state values of the mitoticcompartment, or are depleted according to the kill function of thechemotherapy.

The flow out of the post mitotic compartment (Eq. 20) is similarlydefined as a linear approximation of a product.

IV.C.1. Formulation of the Model as an Optimization Problem for LinearProgramming

The simulation spans a finite number of discrete time steps denoted byT.

We define as the control variable the vector that represents G-CSFadministration at every given hour t: G_(adm) ^(t)tε{1 . . . T}

The objective function is defined as maximization of the followingexpression:

$\begin{matrix}{\sum\limits_{t = 1}^{T}\left( {{\beta^{t} \cdot p^{t}} - G_{adm}^{t}} \right)} & \left( {{Eq}.\mspace{14mu} 24} \right)\end{matrix}$where p^(t) is the number of cells in the post mitotic compartment attime t, and β is a scalar weighting coefficient. The logic forformulating the objective function this way is that the ability tomaintain the post mitotic compartment's steady state size for aprolonged period of time is sufficient for rehabilitation of theNeutrophil lineage as a whole. Also, our goal is to minimize the totaladministered quantity of G-CSF. β is introduced to allow us to factor inboth these goals in one objective. Also, this would allow a differentweight to be given for certain times, e.g. were it determined (byclinicians) that the later states of the post-mitotic compartment shouldbe weighted more than the first ones. Obviously this is only one of thepossible formulations of the objective function as defined in theprevious section.

The pharmacokinetics and pharmacodynamics of G-CSF that were definedgenerally in the mathematical model are defined piecewise linearly. Someof the considerations that was put into formulating these functions werebased directly on experimental evidence (elaborated in the main body oftext). It is noted however, that actual experimental data regarding thedirect effects of G-CSF on the kinetic parameters in which this model isinterested is rather scant. Therefore, some formulations were conductedthrough partly analytic and partly trial-and-error methods.

The formulation of the model in piecewise linear terms will allow use ofthis model as a clinical tool in three ways. First, the model willdetermine the effectiveness of various protocols suggested by cliniciansprior to their actual use on human patients. Second, the model allowscomputation of the optimal protocol in a given situation of Neutrophilcounts, so that the e.g., Neutropenic period following chemotherapy iseither shortened or completely avoided at a minimal cost and exposure toG-CSF. Third, the model serves as a constituent in a broader frameworkof clinical tools that will compute the most optimal treatment plan forchemotherapy and growth factors. These uses should help cliniciansadminister more rational treatment to their patients minimizing bothsuffering and medical costs.

TABLE 1 Kinetics under steady state conditions in healthy humans.Amplification Mean transit Size (10⁶ at the exit time (hours) cells/kgweight) Compartment 2⁺ 24⁻ 0.139* Myeloblasts 2⁺ 48⁻ 0.558*Promyelocytes   1.5⁺ 48⁻ 1.4* Myelocytes 1  160*  5.84* Post mitotic 0   10.96* 0.4* Neutrophils *Dancey, 1976. ⁺Dresch, 1986. ⁻Calculatedbased on the steady state assumption as elaborated in the main text.

IV.D. Cancer and Treatment with Cytotoxic Drug Delivery

IV.D.1. Introduction

Still another embodiment of the present invention deals with cancer andits treatment using chemotherapy. Cancer is the second leading cause ofmortality in the US, resulting in approximately 550,000 deaths a year.There has been a significant overall rise in cancer cases in recentyears, attributable to the aging of the population. Another contributingfactor to the rise in the verifiable number of cases is the wider use ofscreening tests, such as mammography and elevated levels of prostatespecific antigen (PSA) in the blood.

Neither better detection nor the natural phenomenon of aging, however,can entirely explain the increase in new cases of tumors. Meanwhile,other cancers, like brain tumors and non-Hodgkin's lymphoma, arebecoming more common. Their increase could reflect changes in exposuresto as yet unidentified carcinogens. Current trends suggest that cancermay overtake heart disease as the nation's no. 1 killer in theforeseeable future. As gene therapy still faces significant hurdlesbefore it becomes an established therapeutic strategy, present controlof cancer depends entirely on chemotherapeutic methods.

Chemotherapy is treatment with drugs to destroy cancer cells. There aremore than 50 drugs that are now used to delay or stop the growth ofcancer. More than a dozen cancers that formerly were fatal are nowtreatable, prolonging patients' lives with chemotherapy.

Treatment is performed using agents that are widely non-cancer-specific,killing cells that have a high proliferation rate. Therefore, inaddition to the malignant cells, most chemotherapeutic agents also causesevere side-effects because of the damage inflicted on normal bodycells. Many patients develop severe nausea and vomiting, become verytired, and lose their hair temporarily. Special drugs are given toalleviate some of these symptoms, particularly the nausea and vomiting.Chemotherapeutic drugs are usually given in combination with one anotheror in a particular sequence for a relatively short time.

Chemotherapy is a problem involving many interactive nonlinear processeswhich operate on different organizational levels of the biologicalsystem. It usually involves genomic dynamics, namely, point mutations,gene amplification or other changes on the genomic level, which mayresult in increasing virulence of the neoplasia, or in the emergence ofdrug resistance. Chemotherapy may affect many events on the cellularlevel, such as cell-cycle arrest at different checkpoints, celltransition in and out of the proliferation cycle, etc. Chemotherapy mayalso interfere with the function of entire organs, most notably, withbone marrow blood production. In recent years molecular biology andgenetics has made an important step forward in documenting many of theseprocesses. Yet, for assessing the contribution of specific molecularelements to the great variety of disease profiles, experimental biologymust be provided with tools that allow a formal and systematic analysisof the intricate interaction between the genomic, cellular and cellpopulations processes in the host and in the disease agent. This systemis so complex that there is no intuitive way to know how small changesin the drug protocol will affect prognosis. But in spite of thisintricacy, attempts to improve chemotherapy have been carried out by“trial and error” alone, with no formal theory underlying theapplication of specific drug schedules. Such an approach “is apt toresult in no improvement, only discouragement and little usefulinformation for future planning” (Skipper, 1986).

The treatment of cancer by cytotoxic drug (or drug combination) deliveryis addressed. In the current model, two generic types of cells areconsidered: the limiting (i.e. the most drug-sensitive) host cells andthe target cells. Target cells are, in fact, the tumor. Both types ofcells may be damaged while exposed to chemotherapy. The aim is to obtainthe most suitable treatment protocol according to specified conditionsand limitations. It is assumed that the cell dynamics are deterministicand known, and that both types of cells are sensitive tochemotherapeutic agents in certain known period (fraction of thecell-cycle time ranging from 0 to 1) of the cell-cycle (denoted criticalphase). If a cell is exposed to chemotherapy during part of its criticalphase, there is a chance that it will be eliminated, blocked or affectedin any other known way. The description of the dynamics of the delivereddrugs is assumed to be known as well.

In order to achieve the goal optimization process is applied to themodel. The optimization module uses the model predictions in order tosearch for the suitable solution to posted optimization problem. Precisedefining of optimization objectives as well as the relevant parametersadjustment is done according to the settings defined by user/operatorfor every special case. The method can be applied in general cases aswell as in specific ones.

IV.D.2. Model of Biological System

The basic layer of the model incorporates a description of agedistribution of cycling cells and number of resting (quiescent) cells.The term “age of the cell” here refers to chronological age startingfrom the conventional beginning point of mitotic cycle.

Reference is now made to FIG. 13, which is a schematic illustration ofthe tumor cell cycle layer. The whole cycle is divided into 4compartments, or stages (G₁, S, G₂ and M). Each compartment is dividedinto equal subcompartments, where i^(th) subcompartment in each stagerepresents cells of age i in the particular stage (i.e. they have spenti time-steps in this stage). The quiescent stage is denoted G₀. The cellcycle follows a direction as shown by arrows (#). Thus, cells enter eachstage starting with the first subcompartment, denoted G₁.

The model can be described mathematically as follows: Let T_(k) denotethe maximum duration of k^(th) stage in the cycle. Let Δt the symbol isshowing up as a rectangle] denote the time resolution of the model indiscrete time steps. X_(k) ^(i)(t) is a function, which represents thenumber of cells in stage k in the I^(th) sub-compartment, at time t tot+Δt. Both time and age are measured in the same unit, in this case,hours. Let Q(t) represent the number of resting cells at time t to t+Δt.Trans(k,i,t) represents the probability that a cell of age i in thestage k will move to the next (k+1) compartment. Cells entering the newstage always start from the first subcompartment, i.e. from i=1. Thisprobability may change with time, representing the influence ofconditions on cycle length distribution.

By definition, the cell cannot remain more than T_(k) timesteps in thek^(th) compartment, as described in the following equation.∀k:Trans(k,T _(k))=1

The restriction point (R-point) represents a cell's commitment tocomplete to the mitotic cycle. Let T_(R) denote the age at which thecell passes through the restriction point in G1. Only cells in G₁ withI<T_(R) can the cycle (in the absence of a drug).

The total number of proliferating cells P(t) can be calculated asfollows:

${P(t)} = {\sum\limits_{{k = {G\; 1}},S,{G\; 2},M}\left( {\sum\limits_{i = 1}^{T_{k}}{x_{k}^{i}(t)}} \right)}$

In every time interval, quiescent cells may return to the proliferationpool. Alternatively, proliferating cells may change their state tobecome quiescent if and only if they are in the G1 stage and at age i,where T_(R)≧i>0. To describe this process we introduce the functionG_(1□0)(i,t) which describes the number of G1 cells in age i whichbecome quiescent during time interval [t, t+Δt]. This function mayreceive negative values, accounting for cells that return from restingto proliferation.

As it is assumed that the exit to quiescence can occur only prior to theR-point (even in cancer cells), and that a resting cell that returns toproliferation enters the cycle at T₀, it can be stated:∀i>T _(R) ,∀t:G _(1→0)(i,t)=0It must be noted that this function is not dependent on i and t solely.Its value is determined according to current cell distribution and allthe general parameters that characterize the described cells group. Thesame should be said about the values of Trans vector that can changeduring the history of given population.

The model traces the development of described group of cancer cellsusing given parameters, by calculating the number of cells in each andevery subcompartment according to the following stepwise equations:

$\mspace{20mu}{{x_{k}^{i}(t)} = \left\{ {{\begin{matrix}{{{x_{k\;}^{i - 1}\left( {t - 1} \right)} \cdot \left\lbrack {1 - {{Trans}\left( {k,{i - 1},{t - 1}} \right)}} \right\rbrack},} & {1 < i \leq T_{k}} \\{{\sum\limits_{j = 1}^{T_{k - 1}}\left\lbrack {{x_{k - 1}^{j}\left( {t - 1} \right)} \cdot {{Trans}\left( {{k - 1},j,{t - 1}} \right)}} \right\rbrack},} & {i = 1}\end{matrix}{x_{s}^{i}(t)}} = \left\{ \begin{matrix}{{{x_{s}^{i - 1}\left( {t - 1} \right)} \cdot \left\lbrack {1 - {{Trans}\left( {S,{i - 1},{t - 1}} \right)}} \right\rbrack},} & {1 < i \leq T_{G\; 1}} \\{\sum\limits_{j = 1}^{T_{G\; 1}}{\left\lbrack {{x_{G\; 1}^{j}\left( {t - 1} \right)} \cdot {{Trans}\left( {{G\; 1},j,{t - 1}} \right)}} \right\rbrack \cdot \left\lbrack {{1 - {G_{1->0}\left( {{i - 1},{t - 1}} \right)}},} \right.}} & {i = 1}\end{matrix} \right.} \right.}$for k=G₂, M, k−1 returns the previous stage (e.g. G₂−1=S).

These equations make it possible to calculate the number of cells ineach subcompartment at every time interval [t,Δt] starting from initialdistribution (e.g. at time t=0). Since in this model cell ages aremeasured in absolute time units, these measurements refer to thechronological age of the cell, and not the biological age, whose unitsare relative to a maturation rate that differs from cell to cell.Consequently, in this model no cell can remain in the same agesubcompartment after every time step. On the other hand, a fraction ofthe cells that leaves any subcompartment may be transferred to the firstsubcompartment of the next stage, according to probability vectorTrans(k,i,t). This vector provides the ability to account forvariability of cycle lengths while retaining a deterministic approach.

The behavior of the cell populations in this model is completelycontrolled by two components: Trans vector, and G1→G0 function. Thesetwo functions determine uniquely the outcome of every single time step,and, consequently the result over long periods. Thus, they are referredto as “control functions”. The values of these functions may bedependent not only on time and age of cells, but also on the currentpopulation state (or, generally, on the whole history of the population)as well as on the environment associated with a given cell group.However, those parameters are similar for all the cells in the group,implying that the model presented here is suitable for describing highlyhomogenous group of cells. Therefore, the basic layer of the modelshould give a realistic description for a uniform group of cancer cellsfor which environmental conditions and relevant biological propertiesare defined, in a way that will allow the construction of the controlfunctions for the group.

IV.D.3. The General Tumor Model

In the general approach the whole model is viewed as constructed fromsimilar components, each of them derived from the basic structuredescribed in the previous paragraph. Each component represents cellsthat are subjected to the same environmental conditions and, thereforebehaves similarly (to be denoted homogenous group). The whole tumor ismodeled as a union of many different homogenous groups of cells, wherethe development of each group can be accurately predicted (when localconditions are known).

This general model simulates progress of the tumor in discrete steps oftime. At each step the number of cells in each subcompartment of eachgroup is calculated according to the previous state, parameters oftumor, drug concentration, etc. The parameters of the tumor must includeall the information that is relevant to prognosis. Some of theseparameters are defined locally, e.g., those relating to the tumor'sgeometry. For this reason the representation of the spatial structurewill be included.

The cells will be able to pass between the groups during the developmentof the tumor. This allows the representation of the changes in the localconditions during the tumor evolution (e.g. forming of necrotic core,improvement in “living conditions” in vascularized regions, etc.). Inaddition, all the parameters of the tumor may change in accordance withthe dynamics of the cancer.

The calculation of the tumor development over time will be done bystepwise execution of the described simulation and can be used topredict the outcome of the treatment or in fitness function for searchalgorithms.

IV.D.4. From General to Individual Tumor Model

When the general theoretical description of the model is accomplished,the model is fitted to represent the actual tumors. It is renderedpatient-specific by adjusting all the parameters that determine thebehavior of the modeled tumor to those of the real cancer in thepatient's body. In order to accomplish this task we will establish theconnections between mathematical parameters (most of them will havedirect biological implication) and every kind of data that ispractically obtainable in the clinic. These connections may be definedthrough research on statistic correlation between different parameters(including genotype-phenotype correlation), or using advancedbiochemical research showing the relationships between a givenbio-marker and its effects on the reaction rates described by our model.

Thus defined, the model will be able to give realistic predictions fortreatment outcomes either for specific patient or for a broad rangeprofiles of patients and diseases. This tool can serve to perform theprognosis of either an untreated cancer patient, or as a basis fortreatment modeling as is described below.

IV.D.5. Introducing Pharmacology

In order to simulate cancer treatment pharmacologic component is addedto the above model. Pharmacokinetics as well as pharmacodynamics forspecific anticancer drugs are modelled. Cell-cycle specific drugs andcell-cycle unspecific drugs are taken account of by our model.

The distribution of the drug in and around the tumor as well as in theblood (the drug kinetics) are modelled. For this purpose, a suitablemodel is used, defining it precisely for every certain type of the drug.The concentrations of drug in the body are calculated at every time stepin accordance with the drug administration specified by the protocol,and different processes that define drug kinetics in the body.

The dynamics of the drug are represented through the direct influence ofthe drug on tumor cells. The effects on the proliferating cells aremostly blocking the cycle in different stages (which can be modeled ascell arrest) and cell death (immediate or some time after the block).Cell-cycle specific drugs are believed to have no direct influence onquiescent cells, but can affect them indirectly by killing proliferativecells and therefore changing local conditions. Where additional types ofdrugs added to the model, their effect on any kind of cells is modeledas killing certain fraction of cells (which is dose-dependent) orchanging the behavior of the cells.

Additional phenomena that may prove significant in drug kinetics anddynamics (e.g. rate of absorption by the cells, development of tumorresistance to specific drug, angiogenesis etc.) can be introduced intothe model to make it as realistic as needed.

The description of the drug in the model is done in terms ofquantitative functions, which enable to calculate the drug amounts atcertain locations and the tumor response to it at every time step. Inthe general case, these functions include parameters that depend on thespecific data (drug type, body parameters, characteristic of the tumor,etc.) and can be determined in given situation (patient/case).

The combination of cancer model with the limiting normal tissue (seebelow), and the drug model described above makes it possible to predictthe outcome of the treatment, given the relevant parameters for thedrug, the cancer and the patient. Again, the prognosis may be made forspecified cases as well as for broad profiles of patients or disease.This simulation also serves to build the fitness function used for theoptimization objectives.

IV.D.6. Combining with Minimizing Host Toxicity.

Although an accurate predictive tool, the model that representschemotherapy of tumor alone hardly suffice for optimization of drugprotocols. Actually, this model implies using as much drug as possibleuntil the final elimination of the tumor; while in the living system thetoxicity of the drug is the most important constraint limiting thetreatment. In most cases of anticancer chemotherapy the dose-limitingtoxicity is bone marrow suppression, the two most sensitive bone marrowlineages being Granulopoiesis and Thrombopoiesis. Accordingly, those twowere chosen as an example and are modeled separately and in a similarway to predict the negative effect of the chemotherapy on them. These tomodels reconstruct the damage caused by the chemotherapy to the bonemarrow cells and the recovery of these lineages (treated by specificgrowth factors).

Thus, the whole system is capable of predicting the result ofchemotherapy treatment for the tumor as well as for bone marrow cells,allowing the use of the protocols that combine anticancer drugs andgrowth factors for healthy cells.

Chemotherapy toxicity to any other normal host cell populations can besimilarly taken into account, if it is defined as relevant for dose andschedule optimization.

IV.D.7. Individualization of the Models

Due to a great degree of heterogeneity between malignant tumors (evenamong similar tissue types) and between patients, it would beadvantageous to adjust the treatment protocol to the individual case.This individualization procedure includes three aspects:

-   -   1) individual parameters of tumor dynamics.    -   2) individual parameters of patient-specific drug        pharmacokinetics and interaction.    -   3) individual parameters of the dynamics of dose-limiting normal        host tissues.

Relevant data concerning individual cases can be obtained by research onstatistic correlation between different parameters (includinggenotype-phenotype correlation), or using advanced biochemical research(which may establish quantitative relations). In the general model,important dynamic parameters are estimated from experimental studiesconducted in certain patient populations. Any of these parameters, whenavailable on the per patient basis, can be individualized, while thosethat are unavailable can be left as a population-based figure. Thisapproach allows continuous increase in the degree of individualizationof the treatment protocols with progress in the technology of parameterevaluation (e.g., oncochips).

All different parameters may then be adjusted, which will result in anadjusted array of models to be simulated. Parameters may include manydifferent factors, which are adjustable according to the needs of aresearcher or a pharmaceutical company for general use of the treatment,or may even be individualized for use by a specific clinician for aparticular individual. Examples of parameters may include, but are notlimited to age, weight, gender, previous reaction to treatment, desiredpercentage of healthy body cells, desired length of treatment protocol,pathologic or cytologic specifics, molecular markers, genetic markersetc.

In order for the system to be user-friendly, all possible parameters aretermed in ways that are easy for the user to understand.

Once all the parameters are set, an array of solutions is produced basedon the input parameters. A number of possible protocols can be set (isthus generated by the computer). a fitness function is applied, whichresults in scores for each of the proposed solutions.

IV.D.8. Generation of Protocol Space

Referring back to FIG. 2, this model makes it possible to check anygiven treatment protocol and to choose a very good one according touser's criteria. The user may be a physician, a drug developer, ascientist, or anyone else who may need to determine a treatment protocolfor a drug. The specific parameters may include several categories, suchas individual patient characteristics and/or medical history, needs of aspecific user (research, efficacy, treatment, etc.), and otherparticulars (such as maximum length of treatment, confidence level,etc.).

That is, an array of possible treatment protocols is created from whichthe optimal treatment protocol can then be chosen. It should be notedthat the method does not imply the fitness estimation for all possibleprotocols. The use of operation research allows a much moresophisticated, yet resource saving procedure.

An example of this procedure will be described as it relates to cancertreatment by chemotherapy, as described in above-disclosed embodiment ofthe invention. However, it should be noted that a similar procedure maybe performed in any of the embodiments.

The procedure implements cell growth and cell death procedures, asdefined in the detailed model above. There are certain pre-definedparameters, including the lengths of the host and target life-cycles,the lengths of their critical phases, and a resolution factor, thatdetermines the length of a single time unit. The user is asked to definean action (treatment or non-treatment). Simulation of cell growth anddeath is then performed for the single time unit. This procedure isrepeated until the end of the total simulation. Alternatively, thechoice of treatment or non-treatment is made by the processor, with manypossible permutations considered. In that case, the protocol space wouldbe very large, and the resolution would depend on the (selected) lengthof the time unit (and computer capacity)

There are two procedures: one for growth simulation during treatment andone without. The array in which the numbers of cells are kept is updatedonce per time unit, whether with or without treatment present at thattime.

IV.D.9. Defining the Fitness Function

The fitness function is an important tool in Operation Research. In thiscase of protocol optimization, it allows the comparison between a numberof different protocols each one of them scoring differently with respectto various objectives that can be set by the developers or by the usersand identifying the protocol for which the highest weighted score ispredicted. The fitness function calculates for any given protocol itsrelative efficacy (“score” or “fitness”), thus enabling a definitedecision of the best protocol from a given set of protocols.

In different cases, different objectives can be formulated. There areseveral settings in which such a model can be used, including but notlimited to:

-   -   One) clinical practice—where objectives can change depending on        type of disease, condition of the patient, purpose of treatment,        etc.    -   Two) pharmaceutical company—where objectives can be aimed at        finding the therapeutic window and an optimal schedule.    -   Three) scientific setting—research oriented objectives can be        aimed at.

In each case, a particular fitness function can be formulated,reflecting all given requirements. Thus, in any particular case one cancompare between different protocols and obtain the most suitable tohis/her special purposes and needs.

Examples for some alternative objectives are given:

-   -   1. The smallest number of drug dosings required for achieving        any given aim.    -   2. The lowest total drug dose required for achieving any given        aim.    -   3. The minimal total amount of drug needed for rehabilitation.    -   4. The smallest deviation from the baseline at normal cell        populations count (e.g., platlet nadir) after chemotherapy or        another cell-suppressive treatment.    -   5. The shortest period of disease (e.g., Thrombocytopenia).

Using the fitness function it is possible to a) estimate the efficacy ofa given protocol, b) search for the solution of an optimization problem,i.e., predict which protocol will be best of many potential protocolsconsidered for curing/relieving the patient.

IV.D.10. Solving the Optimization Problem

The optimization problem is stated using the described models: to findthe protocol for drug administration (with option to growth factoradministration) which maximizes the given fitness function.

As explained above, the fitness function is defined according to theuser requirements. For example, the goal of the treatment may be definedas minimizing the number of cancer cells at the end of the treatment,minimizing the damage to the BM cells throughout the treatment or at itsend, and curing the patient (where cure is defined precisely) as quicklyas possible. Note that the fitness function may also include goals suchas maximizing life expectancy, minimizing cost of treatment, minimizingtreatment hazards and/or discomfort etc. Generally, the aim ofoptimization is to find the best protocol, i.e. the protocol thatgenerates the best value of fitness. Customarily, this is achieved bymathematical analysis. However, mathematical analysis is restricted toover simplified models, whereas, in order to accommodate biologicallyrealistic parameters, the described models are very complex and,therefore, cannot be solved analytically. On the other hand, thepractical purpose of the treatment is not to find the best possibleprotocol (i.e., the global optimum) but “only” one that will suit theuser's objectives, even if its fitness is not absolutely the best (i.e.,the local optimum). For this reason the solution that can be shown topromise the pre-defined objectives is deemed satisfactory.

Hence, the optimization problem may be reformulated as follows: forgiven initial conditions, find the treatment protocol which will fulfillthe user's requirements (e.g. curing a patient according to givendefinitions of cure) and subjected to given limitations (e.g. treatmentduration, drug amounts, etc.). To this end it is not compulsory to findthe global solution. It is enough, with regards to objectives andlimitations, to perform search, using search algorithms, in certainregions of the protocols' space, and find the local maxima of thefitness function. After determining the locally best protocols, we canverify that they serve one's objectives and check them numerically forstability.

Such a strategy can be used for identifying patient-specific treatment,as well as in the general case, where only the profile of the diseaseand the drug are specified. If more patient-specific data are supplied,the solution will be tailored more specifically. On the other hand, theoptimization program could propose general recommendations for theprotocol types for certain kinds of disease, treated with a certain kindof medication.

It will be appreciated that the present invention is not limited by whathas been described hereinabove and that numerous modifications, all ofwhich fall within the scope of the present invention, exist. Forexample, while the present invention has been described with respect tocertain specific cell lineages, the concept can be extended to any otherlineage and treatment protocol which can be detailed mathematically(e.g., viral or bacterial diseases). Furthermore, certain assumptionswere necessarily used in computing the mathematical models of theembodiments. Values and equations based on these assumptions can bechanged if new information becomes available.

It will be appreciated by persons skilled in the art that the presentinvention is not limited by what has been particularly shown anddescribed herein above. Rather the scope of the invention is defined bythe claims which follow.

Other modifications and variations to the invention will be apparent tothose skilled in the art from the foregoing disclosure and teachings.Thus, while only certain embodiments of the invention have beenspecifically described herein, it will be apparent that numerousmodifications may be made thereto without departing from the spirit andscope of the invention.

The invention claimed is:
 1. A computer system for recommending anoptimal treatment protocol for treating cancer using drugs, for ageneral patient, said system comprising: a cancer system model; atreatment protocol generator for generating a plurality of treatmentprotocols for treating cancer using drugs; a system model modifier,wherein the said system model modifier is adapted to modify said cancersystem model based on parameters specific to a population; and aselector adapted to select an optimal treatment protocol from saidplurality of treatment protocols based on the modified system model; anda computer processor.
 2. The system of claim 1 wherein the system modelfurther comprises: a process model of cancer development; and atreatment model that is adapted to model the effects of treating cancerwith drugs.
 3. The system of claim 2 wherein said process modelincorporates a distribution of cycling cells and quiescent cells.
 4. Thesystem of claim 2 where a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein the system is adapted toensure that cells entering a compartment always enter a firstsub-compartment of the compartment.
 5. The system of claim 4 wherein themodel is adapted to trace development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsub-compartment using stepwise equations.
 6. The system of claim 5wherein the system is adapted to use a probability vector to determine afraction of cells that leaves any sub-compartment in a compartment tomove to a first sub-compartment of the next compartment.
 7. The systemof claim 5 where the system includes a set of control functions that areadapted to uniquely determine an outcome of every single step, whereinsaid control functions comprise age of cells, state of a currentpopulation and associated environment.
 8. The system of claim 5 whereinthe system comprises a model representing a tumor, the model comprisinga combination of a plurality of homogeneous groups of cells, each ofsaid homogeneous groups of cells representing a similarly behaving groupof cells distributed between all the cell-cycle compartments.
 9. Thesystem of claim 1, wherein the system is adapted to calculate in eachstep, a number of cells in each sub-compartment of each compartment ofeach group according to factors including a previous state, parametersof tumor, tumor current microenvironment and drug concentration.
 10. Thesystem of claim 9 where spatial structure of the tumor is included inthe model.
 11. The system of claim 10, wherein the system is adapted toincorporate pharmacokinetics and pharmacodynamics, cytostatic effects,cytotoxic effects, and other effects of anticancer drugs on celldisintegration.
 12. The system of claim 11 wherein the system is adaptedto incorporate a dose-limiting toxicity into the model.
 13. The systemof claim 1, wherein said parameters specific to the general patientcomprise parameters related to tumor dynamics,—drug—pharmacokinetics,pharmacodynamics and dynamics of dose-limiting toxicity in host tissues.14. A computer-implemented method for recommending an optimal treatmentprotocol for treating cancer using drugs for a general patient, saidmethod comprising steps of: creating a cancer system model; enumeratinga plurality of treatment protocols for treating cancer using drugs;modifying the cancer system model based on parameters specific to thegeneral population; selecting an optimal treatment protocol from saidplurality of treatment protocols based on the modified system model; andrecommending said optimal treatment; wherein the steps are performed bya computer.
 15. The method of claim 14 wherein the cancer system modelfurther comprises: a process model of cancer development; and atreatment model that models the effects of treating cancer with drugs.16. The method of claim 15 wherein said process model incorporates adistribution of cycling cells and quiescent cells.
 17. The method ofclaim 15 where a tumor cell cycle is divided into at least fourcompartments G1, S, G2 and M and a quiescent stage is denoted by G0,wherein each of said four compartments is further subdivided intosub-compartments and an ith sub-compartment representing cells of age Iin the corresponding compartment, wherein cells entering a compartmentalways enter a first sub-compartment of the compartment.
 18. The methodof claim 17 wherein the model traces development of cancer cells using apredetermined set of parameters by calculating a number of cells in eachsub-compartment using stepwise equations.
 19. The method of claim 18wherein a probability vector is used to determine a fraction of cellsthat leaves any sub-compartment in a compartment to move to a firstsub-compartment of the next compartment.
 20. The method of claim 18where a set of control functions uniquely determines an outcome of everysingle step, wherein said control functions comprise age of cells, stateof a current population and associated environment.
 21. The method ofclaim 18 wherein a tumor is modeled as a combination of a plurality ofhomogeneous groups of cells, each of said homogeneous groups of cellsrepresenting a similarly behaving group of cells distributed between allthe cell-cycle compartments.
 22. The method of claim 21, wherein in eachstep, a number of cells in each sub-compartment of each compartment ofeach group is calculated according to factors including a previousstate, parameters of tumor, current tumor microenvironment and drugconcentration.
 23. The method of claim 21 where spatial structure of thetumor is included in the model.
 24. The method of claim 23, whereinpharmacokinetics, pharmacodynamics, cytotoxic effects, cytostaticeffects and other effects of anticancer drugs on cell disintegration areincorporated into the model.
 25. The method of claim 24, wherein adose-limiting toxicity is incorporated into the model.
 26. The method ofclaim 14, wherein, said parameters specific to the general patientcomprise parameters related to tumor dynamics, drug pharmacokinetics,pharmacodynamics and dynamics of dose-limiting toxicity in host tissues.27. The method of claim 26, wherein said parameters related to tumordynamics comprise age, weight, gender, percentage of limiting healthycells, desired length of treatment protocol, previous reaction totreatment, molecular markers, genetic markers, pathologic markers andcytologic markers.
 28. The system of claim 13, wherein said parametersrelated to tumor dynamics comprise age, weight, gender, percentage oflimiting healthy cells, desired length of treatment protocol, previousreaction to treatment, molecular markers, genetic markers, pathologicmarkers and cytologic markers.